OPINION

McGREGOR, Justice

¶ 1 Appellant James Van Adams appeals his conviction and death sentence for first-degree premeditated murder. We review this case on direct, automatic appeal pursuant to article VI, section 5.3, of the Arizona Constitution, Arizona Revised Statutes (A.R.S.) section 13-4031(1989), and Rule 31.2.b, Arizona Rules of Criminal Procedure. For the following reasons, we affirm Appellant's conviction and sentence.

I.

¶ 2 On February 9, 1996, police discovered the body of Michelle Lee Anglin, a 5'1", 96 pound, 22 year-old woman, in the master bedroom of a tri-level model home at the Briarwood subdivision of Dave Brown Homes in Phoenix. Ms. Anglin had been working alone at the subdivision as a real estate salesperson that day. After family members were unable to reach her by pager or telephone, Ms. Anglin's sister, a Phoenix police officer, called 911 with a "check welfare" request. The first officers to arrive at the scene found the model home office door unlocked, the lights and music on, and numerous personal items belonging to Ms. Anglin. They conducted a preliminary search of each of the three model homes, and during this first search located three shirt buttons belonging to Ms. Anglin in the third model's upstairs master bedroom closet. The officers also observed that two candles in that model's master bathroom had been knocked over, one into each sink. Everything else appeared undisturbed.

¶ 3 The police then began a more thorough search of the model homes, and particularly of the third model home. They located Ms. Anglin's lifeless, twisted, disrobed body under the third model's master bed and noticed semen stains in that model's master closet. The police found broken ceramic candlesticks and articles of Ms. Anglin's clothing under the bed and saw paint and plaster chips in the master bath and under the bed.

¶ 4 An autopsy revealed no evidence of sexual trauma, but did disclose that Ms. Anglin had been grabbed, choked, and killed by asphyxiation, as evidenced by three bruises to the left side of her neck and one opposing bruise on the right. Both the Phoenix crime laboratory and the Department of Public Safety (DPS) laboratory conducted DNA testing of the carpet sample. Although initial results excluded Appellant as the contributor, and he was so notified, re-testing of the sample by the crime lab produced contradictory results, which included him as a contributor. Additional testing performed by DPS verified the latter result.

¶ 5 Although the police conducted extensive finger and foot printing of the model, none of the prints recovered matched Appellant. Further, none of the witnesses who viewed photo lineups positively identified Appellant as being at the subdivision near the time of death, fixed at between 4:00 p.m. and 5:00 p.m. on February 9, 1996.

¶ 6 The state presented several pieces of evidence to implicate Appellant as Ms. Anglin's assailant. A vehicle license check of Appellant's truck placed him within a few miles of the Briarwood homes on February 9 at approximately 3:25 p.m. Sometime between 3:45 p.m. and 4:15 p.m. on that day, Ms. Anglin, speaking by telephone to another Homes by Dave Brown sales agent, said that a prospective buyer had just arrived at her subdivision. The fellow agent's return calls to Ms. Anglin between 4:30 p.m. and 5:00 p.m. went unanswered. A neighbor, who lived in the subdivision and arrived home from work on February 9 between 4:00 p.m. and 4:15 p.m., recalled seeing a white male exiting the steps of the third model home and noticed a black, Chevrolet, full-sized, older model pickup truck, similar in description to Appellant's, in the model home parking lot. Prospective buyers who visited the subdivision that day between 4:00 p.m. and 4:30 p.m. recalled seeing a man walking from the direction of the second and third model homes and noticed that candlesticks in the third model's master bath had been knocked over and into the sinks. Employment records indicated Appellant either left work on February 9 around noon and failed to return, or left work on February 8 and did not report to work on February 9, after calling in "sick" due to car troubles. Appellant's employer and a co-worker each testified that when they next saw Appellant, a facial injury and black eye that were not present on February 8 or 9 were now evident. Evidence presented at trial also established that Appellant had been to the Briarwood subdivision on previous occasions.

¶ 7 The state also adduced evidence concerning interactions between Appellant and other sales agents several years earlier in California, several months earlier at Briarwood, and several hours prior to Ms. Anglin's murder. Susan Wright, an employee of Homes by Dave Brown, revealed that she had several face-to-face meetings with Appellant at the Briarwood subdivision, and numerous telephone conversations with him while at Briarwood and at another subdivision to which she was transferred. Her first encounter with Appellant at Briarwood occurred in September or October, 1995, at which time Appellant requested that Ms. Wright, who was working alone, accompany him to the third model. Ms. Wright recalled that Appellant stood closer than normal to her and that, although he indicated he had questions about the model, once inside he asked none. Upon the arrival of other prospective buyers, the two immediately left the model and returned to the office. Then, on November 5, 1995, Appellant again visited the subdivision and filled out a guest registration card as "Jim Adams." Appellant made numerous other visits and telephone calls to Ms. Wright, each time asking her out on dates.

¶ 8 Kim Ramos, a young real estate sales associate at a nearby subdivision, testified concerning an encounter she had with Appellant at approximately 2:00 p.m. on February 9, 1996. Appellant arrived at the subdivision in an older model, black Chevrolet truck and asked her to accompany him to the two-story model home to answer some questions. Although Ms. Ramos did accompany him to the model, she testified she was apprehensive and uneasy about Appellant, in part because of how closely he walked next to her. She also stated that she did not spend any appreciable amount of time with him in the model before returning to the sales office, and felt Appellant's questions concerning the model's tile flooring and fourth bedroom/den option were "stupid." Appellant's undisputed visit with Ms. Ramos that day was confirmed by a guest registration card that Appellant filled out at Ms. Ramos' request, on which he listed his name as "James Adams" and provided his correct address and telephone number. Ms. Ramos, who was able to positively identify Appellant and his truck through photographs, told police that at the time she met Appellant none of his facial injuries depicted in the photographs taken after Ms. Anglin's murder existed.

¶ 9 Finally, the state presented the testimony of Melissa Cunningham concerning a 1990 encounter she had with Appellant in California. Ms. Cunningham, a young, petite, 5'4", 102 pound sales agent, was working alone at a new home subdivision when Appellant requested that she accompany him to view the model homes that were still under construction. Appellant said he was particularly interested in a two-story model and its upstairs master bedroom and closet. Ms. Cunningham spent a few minutes with Appellant in that model's master bedroom and closet. As they walked down the stairs, Ms. Cunningham, who was in the lead, heard two thumps, like footsteps, felt a shove, and fell down to the floor below. Appellant apologized, saying that he had tripped on a nail. As both of them searched for the nail, Appellant grabbed Ms. Cunningham from behind, placing one hand around her neck and choking her, while twisting her head to the left with his other hand. He told her he would break her neck if she said anything, dragged her down the hallway and into the kitchen, threw her to the ground, and attempted to sexually assault her, while ripping and tearing her clothes from her body. Ms. Cunningham managed to escape and obtained Appellant's truck license plate number. Appellant was convicted in California of assault with intent to commit rape, a felony. Ms. Cunningham identified Appellant during this trial as her assailant.

II.

¶ 10 Appellant appeals his first-degree murder conviction on nine grounds. For the reasons discussed below, we uphold his conviction.

A.

¶ 11 Appellant first argues that the trial court erred in failing to instruct the jury on the lesser-included offense of second-degree murder. Resting his argument upon Beck v. Alabama, 447 U.S. 625, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980), Appellant asserts that under the evidence, the jury rationally could have found a reasonable doubt as to whether he had premeditated the murder. The Court in Beck reasoned that, in capital murder cases, the jury must be permitted to consider a lesser included offense that is warranted by the evidence before the death penalty will be imposed. See id. at 2389; see also State v. Krone, 182 Ariz. 319, 323, 897 P.2d 621, 625 (1995) (lesser included instruction should be given if "`the jury could rationally fail to find the distinguishing element of the greater offense'") (quoting State v. Detrich, 178 Ariz. 380, 383, 873 P.2d 1302, 1305 (1994)). See also State v. Landrigan, 176 Ariz. 1, 6, 859 P.2d 111, 116 (1993) (" Beck does not require a trial court to instruct on a lesser offense that is unsupported by the evidence."). The distinguishing element between second-degree murder and premeditated murder is premeditation. See Krone, 182 Ariz. at 323, 897 P.2d at 625.

¶ 12 We note initially that the evidence in this case amply supports the jury's premeditated murder conviction. Appellant had been to Briarwood on several occasions prior to February 9, 1996. Police found his semen, along with buttons from Ms. Anglin's top, in the master bedroom closet. Several items of evidence reflected the struggle between Ms. Anglin and her assailant, including the knocked over candles, the broken candlesticks, and the paint chips and plaster found strewn about the floor in the master bath and under the master bed. Injuries to Appellant's face, which did not exist at 2:00 p.m. on February 9, were apparent to Appellant's co-worker on February 10, a fact consistent with Ms. Anglin striking Appellant with the candlesticks. Ms. Anglin's assailant tore off her clothes and placed a choke hold about her neck, strangling her and injuring her neck. He applied sufficient pressure for a sufficient length of time to asphyxiate her. The evidence clearly supports the conclusion that Appellant had sufficient opportunity to reflect upon his actions and could have ceased his attack at any time during the struggle.

¶ 13 Appellant argues, however, that the facts of the California incident support an inference that he did not premeditate Ms. Anglin's murder. He reasons that, in the California assault, he merely pinned his victim down by the neck while attempting the sexual assault. He contends that the jury could have concluded that, as in the earlier incident, he intended to stop his assault on Ms. Anglin short of murder. He concludes that although he may have known Ms. Anglin was dying of asphyxiation, he did not premeditate that result, and thus the jury could have concluded that he committed intentional or knowing second-degree murder, rather than premeditated first-degree murder.

¶ 14 Even if we thought a jury could rationally accept that argument, the outcome here would not change. Appellant's theory of defense throughout trial and on appeal was mistaken identity; he denied all involvement in the murder. At no time did he argue lack of premeditation or claim that he innocently or mistakenly committed the acts. As we have previously concluded, when the "defendant's theory of the case denies all involvement in the killing, and [when] no evidence provides a basis for a second degree murder conviction, . . . [and] the record is such that defendant is either guilty of the crime charged or not guilty," refusal to issue the instruction is proper. State v. Salazar, 173 Ariz. 399, 408, 844 P.2d 566, 575 (1992).

¶ 15 The trial court properly concluded that, under these facts, a second-degree murder instruction would be inappropriate. We find no error.

B.

¶ 16 Appellant next asserts that the trial court erred in failing to instruct the jury that premeditation requires actual reflection. See State v. Ramirez, 190 Ariz. 65, 70, 945 P.2d 376, 381 (App. 1997). Appellant contends that the trial court's instruction improperly reduced the state's burden of proof and improperly focused on the length of time required for premeditation. Appellant concedes that he did not object to the premeditation instruction as given at trial and as described by the state in its closing argument, but contends that giving it constituted fundamental error.

¶ 17 We have previously held that rarely will an improperly given instruction "`justify reversal of a criminal conviction when no objection has been made in the trial court.'" State v. Zaragoza, 135 Ariz. 63, 66, 659 P.2d 22, 25 (1983) (quoting Henderson v. Kibbe, 431 U.S. 145, 154, 97 S.Ct. 1730, 1736, 52 L.Ed.2d 203, 212 (1977)). Failure of a criminal defendant to object to an instruction precludes him from claiming error on appeal absent fundamental error. See Ariz.R.Crim.P. 21.3.c; State v. Chavez, 143 Ariz. 238, 239, 693 P.2d 893, 894 (1984); Zaragoza, 135 Ariz. at 66, 659 P.2d at 25. Fundamental error exists when the error "`goes to the foundation of the case, or . . . takes from a defendant a right essential to his defense.'" State v. Wussler, 139 Ariz. 428, 430, 679 P.2d 74, 76 (1984) (citing State v. Mincey, 130 Ariz. 389, 397, 636 P.2d 637, 645 (1981)); State v. Grilz, 136 Ariz. 450, 454, 666 P.2d 1059, 1063 (1983).

¶ 18 Appellant's defense rested solely on his claim of total innocence or mistaken identity, rather than on an assertion that although he committed the murder, he did so mistakenly or without actual reflection. The premeditation instruction therefore neither removed a right from Appellant nor hindered his ability to raise total innocence or mistaken identity as his defense. If the trial court erred, the error did not take from defendant a right essential to his defense. We find no fundamental error.

C.

¶ 19 Appellant next argues that the trial court abused its discretion by admitting evidence of Appellant's other acts in violation of Rule 404(b), Arizona Rules of Evidence, and by failing to give the jury a proper limiting instruction. The trial court admitted evidence of Appellant's prior assault on Melissa Cunningham to prove identity, modus operandi, intent, knowledge, opportunity and preparation, noting that this incident was "remarkably similar" to the attack on Ms. Anglin and was "both unusual and distinctive to appear as if like a signature," and of his encounter with Kim Ramos to prove identity.

¶ 20 We review admission of Rule 404(b) evidence under an abuse of discretion standard. See State v. Gulbrandson, 184 Ariz. 46, 60, 906 P.2d 579, 593 (1995). Evidence of prior acts is admissible if it is relevant and "admitted for a proper purpose." Id. (referencing Huddleston v. United States, 485 U.S. 681, 691, 108 S.Ct. 1496, 1502, 99 L.Ed.2d 771, 783 (1988)). Evidence is relevant if it tends to make a material fact more or less probable than it would be absent the evidence. See Ariz. R. Evid. 401 (1997). When "similarity of the crimes is [a] basis for the relevance of the evidence," the other crime "must be similar to the offense charged" and the similarities must exist when normally differences would be expected to be found. Gulbrandson, 184 Ariz. at 61, 906 P.2d at 594; State v. Williams, 182 Ariz. 548, 552, 898 P.2d 497, 501 (App. 1995). Although evidence of prior acts may not be used to prove the defendant's propensity to commit the crime, it is admissible when used to prove the defendant's "motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident." Ariz. R. Evid. 404(b) (West Supp. 1998); State v. Roscoe, 184 Ariz. 484, 491, 910 P.2d 635, 642 (1996); Gulbrandson, 184 Ariz. at 61, 906 P.2d at 594; Williams, 182 Ariz. at 552, 898 P.2d at 501; State v. Terrazas, 189 Ariz. 580, 582, 944 P.2d 1194, 1196 (1997).

¶ 21 Numerous similarities exist between Ms. Anglin's, Ms. Cunningham's and Ms. Ramos' encounters with Appellant. At the time they met Appellant, all three women were young sales agents working alone in a residential real estate sales office. Both Ms. Cunningham and Ms. Anglin were petite. All three incidents occurred during the day. In the cases of Ms. Cunningham and Ms. Ramos, Appellant requested that they accompany him upstairs in the two-story model. In Ms. Cunningham's case, this involved accompanying him to the master bedroom and closet. Evidence found in proximity to Ms. Anglin's body permits the inference that he made the same request of her. Appellant physically attacked both Ms. Anglin and Ms. Cunningham by placing his right hand about their necks. In both instances, the assailant ripped off the victim's clothes and attempted to gratify himself sexually. Ms. Ramos' testimony and description of Appellant's vehicle, which assisted in placing Appellant in the vicinity of the Briarwood homes near the time of Ms. Anglin's murder, also related to identity. While nothing in the record clearly establishes, as the state contends, that Ms. Ramos was Appellant's first intended victim and that her "quick wits" and "feelings of uneasiness" caused Appellant to seek another victim, her testimony did assist the jury in finding both opportunity and intent. Because Melissa Cunningham's and Kim Ramos' testimonies tended to prove Appellant's identity and establish Appellant's opportunity and intent, the evidence was relevant and admitted for a proper purpose.

¶ 22 The third factor we consider is whether the trial court should have excluded the prior acts evidence, notwithstanding its relevance and admissibility for a proper purpose, because of the danger of unfair prejudice. See State v. Fernane, 185 Ariz. 222, 226, 914 P.2d 1314, 1318 (App. 1995) (otherwise admissible evidence may be excluded if its probative value substantially outweighs the danger of unfair prejudice). Courts must ensure that the defendant's guilt is not proven "through excessively prejudicial evidence of other acts," including evidence that tends to suggest that the jury should reach its "decision on an improper basis, such as emotion, sympathy, or horror." State v. Ives, 187 Ariz. 102, 111, 927 P.2d 762, 771 (1996); Gulbrandson, 184 Ariz. at 61, 906 P.2d at 594.

¶ 23 Here, Ms. Cunningham's testimony encompassed no inflammatory remarks concerning Appellant. The same cannot as easily be said of Ms. Ramos' testimony. The trial judge permitted Ms. Ramos to testify that she felt uneasy about Appellant because he walked closely to her. She also stated that she did not believe he intended to buy a house because of his clothing, the vehicle he drove, and the questions he asked about the flooring and fourth bedroom, which she characterized as stupid. This portion of her testimony was not related either to identity or to opportunity and may well have lacked probative value. These statements, however, constituted only a small portion of her overall testimony. In the remainder of her testimony, Ms. Ramos conveyed that on the day of Ms. Anglin's murder, Appellant arrived at her subdivision, which was near the Briarwood homes, around 2:00 p.m. Ms. Ramos, a young sales agent, was working alone that day. Appellant asked her to accompany him to the two-story model home to answer questions. Once inside that model, Appellant asked Ms. Ramos about the flooring before proceeding upstairs with her, where he asked about bedroom options. The probative value of this testimony in relation to establishing Appellant's identity, or "fingerprint," was not outweighed by prejudicial unfairness. Any error that may have occurred in relation to Ms. Ramos' emotional testimony was harmless. See State v. Atwood, 171 Ariz. 576, 639, 832 P.2d 593, 656 (1992) (harmless error exists when there is no "`reasonable probability . . . that a verdict might have been different had the error not been committed'") (quoting State v. Williams, 133 Ariz. 220, 225, 650 P.2d 1202, 1207 (1982).

¶ 24 Appellant also argues that the incident involving Ms. Cunningham was too remote in time to be relevant to Ms. Anglin's murder and, therefore, admitting evidence of it unfairly prejudiced him. The incident between Appellant and Ms. Cunningham occurred in 1990, and Appellant remained incarcerated for it until 1991 or 1992. Although remoteness between the two incidents affects the weight to be given the testimony by the jury, it generally does not determine its admissibility. See Fernane, 185 Ariz. at 225, 914 P.2d at 1317 (finding that "[a]n assertion that a prior act is too different or too remote in time from the charged offense goes `to the weight of the evidence,'" and not to relevance or admissibility); State v. Hinchey, 165 Ariz. 432, 435-36, 799 P.2d 352, 355-56 (1990). In this instance, the trial judge's decision to permit the jury to consider how much weight to give Appellant's prior act, which preceded Ms. Anglin's murder by nearly six years, did not result in unfair prejudice.

¶ 25 Finally, when the trial judge admits evidence of prior acts, an "objecting party must have the opportunity to receive a limiting instruction if requested." Gulbrandson, 184 Ariz. at 60, 906 P.2d at 593. Appellant asked for and received the following limiting instruction:

Evidence of other acts of the defendant has been admitted in this case. You must not consider this evidence to prove defendant's character or that the defendant acted in conformity with that character. You may, however, consider that evidence only as it relates to the defendant's opportunity, intent, preparation, knowledge or identity.

Although Appellant did not object to this instruction at trial, he now asserts that the trial judge erred in failing to further limit the jury's consideration of the Cunningham testimony to whether it proved his identity and modus operandi and failed to distinguish between the Cunningham and Ramos incidents. Appellant asserts that, without these more specific instructions, the jury could have concluded that Appellant had a character trait of attacking women for sexual gratification and acted in conformity with that trait on this occasion. Alternatively, he contends, the jury may have been so outraged by his prior conduct that they improperly based their guilty verdict upon that reaction. Appellant's contentions are unconvincing.

¶ 26 By utilizing the disjunctive conjunction "or," the trial court denoted several alternatives that the jury could consider in arriving at their conclusions about the prior acts evidence. The jury could have disregarded all the alternatives if they determined that the evidence fell outside the instruction. Further, the instruction admonished the jury to refrain from improperly considering the evidence as proving a character trait. Nothing in the record indicates that the jury failed to comply with this admonition. The trial court did not abuse its discretion in admitting evidence of Appellant's prior acts.

D.

¶ 27 Having objected neither to the court's ruling permitting death qualification of the jury nor to the court's discussion of jury death qualification during voir dire, Appellant now contends the trial court abused its discretion by death qualifying the jurors. As Appellant concedes, we have previously rejected the argument that, because the judge determines the defendant's sentence, the jury should not be death qualified. See State v. LaGrand, 153 Ariz. 21, 33, 734 P.2d 563, 575 (1987). We have also repeatedly reaffirmed our agreement with Witherspoon v. Illinois, 391 U.S. 510, 522 n. 21, 88 S.Ct. 1770, 1777 n. 21, 20 L.Ed.2d 776, 785 n. 21 (1968) and Adams v. Texas, 448 U.S. 38, 45, 100 S.Ct. 2521, 2526, 65 L.Ed.2d 581, 589 (1980), which held that questioning jurors is permissible to determine if they can uphold their duties, follow the court's instructions, and render a decision in accordance with their oath. See State v. Martinez-Villareal, 145 Ariz. 441, 449, 702 P.2d 670, 678 (1985) (questioning jury to determine whether bias exists is permissible); State v. Schaaf, 169 Ariz. 323, 331, 819 P.2d 909, 917 (1991) (juror questioning is permissible to determine whether their performance will be "substantially impair[ed]" by their views); Atwood, 171 Ariz. at 624, 832 P.2d at 641 (citing Martinez-Villareal and referencing State v. White, 168 Ariz. 500, 509, 815 P.2d 869, 878 (1991)); Gulbrandson, 184 Ariz. at 57, 906 P.2d at 590 (death qualifying jurors to determine if they can perform their duties is permissible and does not constitute fundamental error).

¶ 28 Nonetheless, Appellant requests that we revisit the issue, in light of the United States Supreme Court's ruling in Lockhart v. McCree, 476 U.S. 162, 175-76, 106 S.Ct. 1758, 1766-67, 90 L.Ed.2d 137, 149 (1986) and its footnote reference to Rector v. State, 280 Ark. 385, 396-97, 659 S.W.2d 168, 173-74 (1983), both of which uphold the constitutionality of death qualifying a jury in a capital case. We see no reason to reconsider our prior holdings.

E.

¶ 29 Although Appellant also failed to object to the "reasonable doubt" instruction tendered by the trial court, he now challenges the constitutionality of the reasonable doubt instruction we approved in State v. Portillo, 182 Ariz. 592, 898 P.2d 970 (1995). Relying in part upon State v. Perez, 1998 WL 847995 (Haw.App. Oct. 23, 1998), recently affirmed by the Supreme Court of Hawai'i in State v. Perez, 1999 WL 56006 (Feb. 8, 1999), Appellant asserts that we must specifically address the use of the language "firmly convinced" in defining "proof beyond a reasonable doubt," and consider whether that language improperly reduces the state's burden of proof to "clear and convincing evidence."

¶ 30 The trial court based its instruction upon the instruction we adopted in Portillo. We have clearly indicated our preference for this instruction, which is based upon the Federal Judicial Center's proposed instruction. The trial court satisfied the requirements we specified in Portillo and did not err.

F.

¶ 31 Appellant's next contention is that the trial court, after conducting a consolidated four-day Frye hearing in four cases, erred in concluding that the DPS's protocol for PCR testing is generally accepted by the scientific community and the results are admissible. We previously have recognized the scientific principles of RFLP methodology in DNA analysis as generally accepted by the relevant scientific community. See State v. Bible, 175 Ariz. 549, 590, 858 P.2d 1152, 1193 (1993) (concluding that "the principles and theory underlying DNA testing . . . are generally accepted in the relevant scientific community," thereby permitting "judicial notice of DNA theory and the [RFLP] techniques [used] . . . for ascertaining and declaring a match"); State v. Johnson, 186 Ariz. 329, 922 P.2d 294 (1996) (noting that RFLP principles are generally accepted and valid); State v. Hummert, 188 Ariz. 119, 933 P.2d 1187 (1997) (recognizing this Court's acceptance of DNA evidence using RFLP methodology); State v. Bogan, 183 Ariz. 506, 905 P.2d 515 (App. 1995) (acknowledging that Arizona has held RFLP to be generally accepted in the scientific community).

¶ 32 In 1995, Arizona first addressed PCR principles and determined that the relevant scientific community generally accepted RAPD, a methodology applying PCR technology, "as sound technology." Bogan, 183 Ariz. at 511, 905 P.2d at 520. Since then, we have considered the "reverse dot blotting" technique utilized in the DQ-alpha PCR methodology, finding that PCR technology generally, and the DQ-alpha methodology specifically, are "generally accepted within the relevant scientific community for use on crime scene evidence." Tankersley, 191 Ariz. at 363, 365, 956 P.2d at 490, 492.

¶ 33 Arizona has not been alone in recognizing PCR technology as generally accepted in the relevant scientific community. Numerous state and federal courts have admitted expert testimony concerning PCR technology and, in some instances, have determined that the general reliability of PCR technology may be judicially noticed. See United States v. Shea, 957 F. Supp. 331, 339 n. 20 (D.C. N. H. 1997). See also State v. Lyons, 324 Or. 256, 273, 924 P.2d 802, 812 (1996) (noting that several appellate decisions have affirmed the use of PCR testing methods).

¶ 34 Appellant contends that, despite our acknowledgment and acceptance of PCR technology generally, we have not yet addressed his specific criticisms of the PCR methods employed by DPS in his case and must now do so. Appellant's arguments, however, challenge DPS's application of the PCR methodologies to the evidence in this matter, and therefore attack the weight and credibility to be accorded the evidence by the jury, not its admissibility. The task of the court is to determine whether a particular approach garners general acceptance in the relevant scientific community. See Bible, 175 Ariz. at 580, 858 P.2d at 1183 (noting that once a trial court conducts a Frye hearing and concludes that the scientific principles are generally accepted by the relevant scientific community, the "scientific evidence is admissible `subject to a foundational showing'") (quoting State ex rel. Collins v. Superior Court, 132 Ariz. 180, 196, 644 P.2d 1266, 1282 (1982)). Once that decision is made, we leave to the parties and their witnesses, and ultimately to the jury, the task of weighing the significance of any errors that may have occurred in applying generally accepted principles to the facts of a particular case. We find no error.

G.

¶ 35 Next, Appellant challenges the trial court's use of a prior California conviction to aggravate his sentence. He argues that because the record of the California conviction included no photographs or fingerprints of the perpetrator and did not reference the victim's name or the circumstances surrounding the incident, the state failed to satisfy its burden of proof.

¶ 36 Our law on this point is clear. To utilize a prior conviction to aggravate Appellant's sentence, the state must prove that Appellant and the perpetrator of the California crime were one and the same and that a prior conviction actually occurred. See State v. Pennye, 102 Ariz. 207, 208, 427 P.2d 525, 526 (1967) (citing State v. Salazar, 3 Ariz. App. 114, 117, 412 P.2d 289, 292 (1966)), overruled in part by Smith v. Eyman, 104 Ariz. 296, 451 P.2d 877 (1969). The state can make that showing through the use of extrinsic evidence, including "a certified copy of a judgment of conviction." State v. Nash, 143 Ariz. 392, 403, 694 P.2d 222, 233 (1985).

¶ 37 The state introduced a certified copy of California's Disposition of Arrest and Court Action that listed "Adams, James Van," "dob 1/30/64," as the person charged with assault with intent to commit rape. The documents also confirm that the social security number contained in California's records matches Appellant's. Although the state introduced no photographs or fingerprints of the "Adams, James Van" convicted in California, and the California record does not include the name of the victim or particulars of the incident, California's record sufficiently identified Appellant as the perpetrator. His name, description and date of birth all match the records held by the City of Phoenix. In addition, the state called Ms. Cunningham as a trial witness, and she identified Appellant as her assailant. No error occurred.

H.

¶ 38 Appellant also challenges the trial court's finding that his California conviction for assault with intent to commit rape constituted a serious offense under A.R.S. § 13-703.F.2 and could be used as an aggravating factor.

¶ 39 To determine whether an "F.2" aggravating circumstance exists, we compare the statutory definition of the prior offense to A.R.S. sections 13-703.F.2 and 13-703.H.5. See State v. Ysea, 191 Ariz. 372, 375, 956 P.2d 499, 502 (1998). Under A.R.S. section 13-703.F.2 (West Supp. 1998), a defendant's "previous convict[ion] of a serious offense, whether preparatory or completed" constitutes an aggravating factor. Section 13-703.H.5 defines "serious offense" as including "sexual assault." Thus, to constitute a "serious offense" in Arizona, the California conviction must have constituted a "sexual assault" or "attempted sexual assault." See A.R.S. §§ 13-703.F.2 and 13-703.H.5.

¶ 40 As the parties acknowledge, Appellant was convicted under California's Penal Code section 220 for assault with intent to commit rape. California Penal Code sections 240 and 261 define the terms used in section 220. Section 240 defines "assault" as "an unlawful attempt, coupled with a present ability, to commit a violent injury on the person of another," and section 261 defines "rape" as "an act of sexual intercourse," which can be accomplished through a number of enumerated ways. Therefore, Appellant was convicted in California of an unlawful attempt to commit a "violent injury on the person of another" in the form of "an act of sexual intercourse."

¶ 41 Sexual assault in Arizona is committed by "intentionally or knowingly engaging in sexual intercourse or oral sexual conduct with any person without consent of such person." A.R.S. § 13-1406. A (West Supp. 1998). "Attempt," on the other hand, is a preparatory offense that is "separate and distinct from [the] substantive offense," and exists when a person intentionally takes steps intended to "culminate in the commission of an offense." A.R.S. § 13-1001.A.2 (1989); State v. Tellez, 165 Ariz. 381, 383, 799 P.2d 1, 3 (App. 1989). To qualify as a serious offense, then, Appellant's California conviction must constitute either the intentional or knowing engagement in non-consensual sexual intercourse or oral sexual conduct with another, or steps intentionally taken in an effort to accomplish those results.

¶ 42 Arizona's sexual assault statute recognizes that the use of violence is one of several factors that negate consent. Appellant's California conviction establishes that he deliberately took steps intended to culminate in non-consensual sexual conduct with another person, which constitutes attempted sexual assault under Arizona law. No error resulted when the trial court concluded that Appellant's California conviction constituted a "serious offense" pursuant to A.R.S. section 13-703.F.2.

¶ 43 Appellant also claims the trial court erred by relying upon Ms. Cunningham's testimony to establish the prior conviction. While we agree that the trial court should not have considered Ms. Cunningham's testimony for this specific purpose, no reversible error resulted. See Richmond, 180 Ariz. at 578, 886 P.2d at 1334 (citing State v. Henry, 176 Ariz. 569, 587, 863 P.2d 861, 879 (1993) and its holding that "[t]he statutory definition of the prior crime and not its specific factual basis, dictates whether an aggravating circumstance exists under A.R.S. § 13-703(F)(2)."). As we previously noted, Ms. Cunningham's testimony was admissible to establish Appellant's identity and reinforced the record evidence that identified Appellant as her assailant. It was not needed to establish any element of the California conviction. Any consideration that the trial court may have given Ms. Cunningham's testimony resulted in harmless error.

I.

¶ 44 Finally, asserting that not all strangulations are per se cruel and that not all murders involving sexual assault automatically fall within the scope of A.R.S. section 13-703.F.6, Appellant urges that the trial court erred in concluding that he murdered Ms. Anglin in an especially cruel manner. "Cruelty refers to the pain and suffering that the victim experiences before death." State v. Ramirez, 178 Ariz. 116, 129, 871 P.2d 237, 250 (1994); State v. Gretzler, 135 Ariz. 42, 51, 659 P.2d 1, 10 (1983) (cruelty focuses upon the victim's suffering and mental anguish). Cruelty requires conclusive evidence that the victim was conscious during the infliction of violence and experienced significant "uncertainty as to [her] ultimate fate." State v. Amaya-Ruiz, 166 Ariz. 152, 177, 800 P.2d 1260, 1285 (1990); State v. Towery, 186 Ariz. 168, 188, 920 P.2d 290, 310 (1996). Time alone is not determinative; we have previously found cruelty where the victim suffered for a period as short as eighteen seconds or three minutes. See State v. Herrera, 176 Ariz. 21, 34, 859 P.2d 131, 144 (1993). The defendant either must intend the victim's pain or anguish or must "reasonably foresee that there is a substantial likelihood that the victim will suffer as a consequence of the defendant's acts." State v. Adamson, 136 Ariz. 250, 266, 665 P.2d 972, 988 (1983). We consider the "entire murder transaction and not simply the final act that killed the victim." State v. Lavers, 168 Ariz. 376, 393, 814 P.2d 333, 350 (1991).

¶ 45 Here, the record reveals that a struggle took place between Appellant and Ms. Anglin in the master closet and bath. The location of the buttons and semen in the master closet, the damaged candles and candlesticks in the master bath area, and paint and ceramic chips from the master bathroom in both the bathroom and under the master bed, provide evidence of the scope of the struggle between Ms. Anglin and Appellant. The torn, knotted, and intertwined condition of Ms. Anglin's clothes indicate they were forcibly ripped from her body. She sustained numerous abrasions and contusions to various parts of her body, some of which substantiate that force was used in removing her clothes. Injuries to her hands and wrists signify that she struggled and attempted to defend herself. Only after this struggling occurred did Appellant apply sufficient force to strangle her to death. The Chief Medical Examiner testified that it typically takes two to three minutes, but not less than ninety seconds, for a strangulation victim to lose consciousness. Until that time, Ms. Anglin undoubtedly was uncertain as to her ultimate fate. See Towery, 186 Ariz. at 188, 920 P.2d at 310. From these facts, the trial court concluded beyond a reasonable doubt that Ms. Anglin was conscious during at least a portion of the attack and that Appellant intended to, and in fact did, inflict upon her both mental and physical pain.

¶ 46 The evidence substantially supports the trial court's conclusions. At least some of Ms. Anglin's injuries were inflicted while she was yet conscious and struggling. Equally evident is that she suffered pain and terror at the hands of Appellant, especially as she attempted to break free of him in the bathroom and while he choked her. As Appellant points out, the expert testimony did not establish which injuries, other than those to the neck, necessarily occurred before death. That factor, however, affects the strength of the cruelty factor, not its existence. See State v. McKinney, 185 Ariz. 567, 578, 917 P.2d 1214, 1225 (1996) (when conducting an independent review of the evidence, consideration is given to the "quality and the strength" of the aggravating and mitigating factors). The record makes clear the fact that Appellant inflicted injuries upon Ms. Anglin prior to her losing consciousness. We therefore conclude that the trial court appropriately found the aggravating factor of cruelty.

II.

¶ 47 Appellant contends that the trial court erred when it imposed the death penalty. For the following reasons, we uphold the trial court's decision.

A.

¶ 48 We first consider whether the trial court failed to properly weigh the aggravating and mitigating evidence. We engage in this determination by independently reviewing the aggravating and mitigating circumstances. See A.R.S. § 13-703.01 (West Supp. 1998). See also Adamson, 136 Ariz. at 266, 665 P.2d at 988 (this court "independently determine[s] if the trial court correctly applied aggravating and mitigating circumstances").

¶ 49 The trial court found two aggravating factors. First, the California conviction constituted a "serious offense." A.R.S. § 13-703.F.2. Second, Appellant committed Ms. Anglin's murder in an especially cruel manner. See A.R.S. § 13-703.F.6 (West Supp. 1998). As previously noted, we uphold both of these findings.

¶ 50 We next evaluate the mitigating evidence. Trial judges, when sentencing a defendant, must consider all statutory and relevant non-statutory mitigating factors that a defendant proffers. See Gulbrandson, 184 Ariz. at 69, 906 P.2d at 602; State v. Fierro, 166 Ariz. 539, 551, 804 P.2d 72, 84 (1990). Trial judges possess discretionary power to determine the weight to be given each mitigating factor proven by a preponderance of the evidence. See State v. Hyde, 186 Ariz. 252, 282, 921 P.2d 655, 685 (1996).

¶ 51 Appellant refused to present mitigating evidence. Responding to the trial judge's questioning, Appellant expressly stated that he understood his right to present mitigating evidence, voluntarily waived his right to present such evidence, and specifically instructed his counsel not to do so. He likewise instructed his family not to cooperate with his counsel's efforts to investigate his background for purposes of presenting mitigation to the court. Notwithstanding this lack of cooperation and evidence, Appellant's counsel did advise the trial judge that Appellant, who was then separated, but not divorced, from his wife and child, planned a reconciliation.

¶ 52 Trial judges must be permitted to consider, "as a mitigating factor, any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death." Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 2964-65, 57 L.Ed.2d 973, 990 (1978) (emphasis omitted). Neither Appellant nor the record offers us any factors or circumstances of the offense that would warrant imposing less than a sentence of death in this case.

¶ 53 After independently considering the sole mitigating circumstance offered by Appellant's counsel, we hold that it does not sufficiently outweigh the aggravating factors of cruelty and the existence of a serious offense. We therefore affirm the sentence.

B.

¶ 54 Appellant also raises fourteen challenges to the validity of Arizona's capital sentencing scheme, asserting it is facially unconstitutional. Despite Appellant's failure to offer any arguments in support of his challenges, and our resultant ability to deem these issues waived, we address them briefly to note that we are unpersuaded to reconsider our prior decisions concerning these challenges.

¶ 55 First, Appellant contends the death penalty is per se cruel and unusual punishment. Both the United States Supreme Court and this court have rejected this argument. See Gregg v. Georgia, 428 U.S. 153, 186-87, 96 S.Ct. 2909, 2931, 49 L.Ed.2d 859, 882 (1976); Salazar, 173 Ariz. at 411, 844 P.2d at 578; State v. Gillies, 135 Ariz. 500, 507, 662 P.2d 1007, 1014 (1983). Second, Appellant asserts that execution by lethal injection is cruel and unusual punishment. This court has previously determined lethal injection to be constitutional. See State v. Hinchey, 181 Ariz. 307, 315, 890 P.2d 602, 610 (1995). Next, Appellant asserts that the statute unconstitutionally requires imposition of the death penalty whenever at least one aggravating circumstance and no mitigating circumstances exist. We previously rejected this challenge. See State v. Bolton, 182 Ariz. 290, 310, 896 P.2d 830, 850 (1995); State v. Miles, 186 Ariz. 10, 19, 918 P.2d 1028, 1037 (1996). See also Walton v. Arizona, 497 U.S. 639, 648, 110 S.Ct. 3047, 3049-50, 111 L.Ed.2d 511, 525 (1990) (noting that because Arizona's aggravating factors are standards to guide sentencing, "the judge's finding of any particular aggravating circumstance does not require the death penalty, and the failure to find any particular aggravating circumstance does not preclude that penalty"). Fourth, Appellant attacks the statute's constitutionality for its failure to permit defendants to "death qualify" the sentencing judge. We rejected an identical claim in State v. West, 176 Ariz. 432, 454-55, 862 P.2d 192, 214-15 (1993). Appellant's fifth challenge is the statute's allegedly unconstitutional failure to guide the sentencing court. We previously held that the death penalty statute narrowly defines death-eligible persons as those convicted of first-degree murder, where the state has proven one or more statutory aggravating factors beyond a reasonable doubt. See State v. Greenway, 170 Ariz. 155, 164, 823 P.2d 22, 31 (1991). Appellant's sixth argument is that Arizona's death penalty statute unconstitutionally requires defendants to prove that their lives should be spared. We rejected an identical claim in State v. Fulminante, 161 Ariz. 237, 258, 778 P.2d 602, 623 (1988). Next, Appellant asserts that the statute unconstitutionally fails to require either cumulative consideration of multiple mitigating factors or that the trial court make specific findings as to each mitigating factor. The state responds that the trial court must consider all relevant mitigation evidence, but the weight to be given such evidence rests in the judge's discretion. Although aggravating factors were found, Appellant essentially offered no mitigation evidence. Appellant's contention is meritless. See Gulbrandson, 184 Ariz. at 69, 906 P.2d at 602; Ramirez, 178 Ariz. at 131, 871 P.2d at 252; Fierro, 166 Ariz. at 551, 804 P.2d at 84. We previously rejected Appellant's eighth argument that Arizona's death penalty statute insufficiently channels the sentencer's discretion in imposing the death sentence. See West, 176 Ariz. at 454, 862 P.2d at 214; Greenway, 170 Ariz. at 164, 823 P.2d at 31. Next, Appellant asserts that Arizona's death penalty statute is unconstitutionally defective because it fails to require the state to prove that death is appropriate. We rejected that argument in Gulbrandson, 184 Ariz. at 72, 906 P.2d at 605. Although Appellant claims the statute is unconstitutional because the aggravating factor of "cruel, heinous or depraved" as provided in A.R.S. section 13-703.F.6 is vague and fails to perform a narrowing function, the United States Supreme Court has upheld the F.6 factor as interpreted by this court. See Walton, 497 U.S. at 652-56, 110 S.Ct. at 3056-58, 111 L.Ed.2d. at 527-30. See also State v. Mata, 185 Ariz. 319, 323, 916 P.2d 1035, 1039 (1996) (holding F.6 factor, as construed, gives sentencer adequate guidance). Appellant next contends Arizona's statutory scheme for considering mitigating evidence is unconstitutional because it limits full consideration of that evidence. We have rejected this contention. See State v. Mata, 125 Ariz. 233, 242, 609 P.2d 48, 57 (1980). Appellant also asserts the prosecutor's discretion to seek the death penalty unconstitutionally lacks standards. Neither Appellant nor the state offers any argument on this issue, and we rejected a similar claim in Salazar, 173 Ariz. at 411, 844 P.2d at 578. Next, Appellant contends that Arizona's death sentence has been applied in a discriminatory manner against impoverished males whose victims have been Caucasian. We rejected the argument that the death penalty has been applied in a discriminatory manner in West, 176 Ariz. at 455, 862 P.2d at 215. Finally, Appellant asserts that the Constitution requires a proportionality review of a defendant's death sentence. We have previously considered and rejected this argument. See Salazar, 173 Ariz. at 416, 844 P.2d at 583 (noting that "no statute requires or suggests proportionality reviews in death cases"); State v. Serna, 163 Ariz. 260, 269-70, 787 P.2d 1056, 1065-66 (1990) (United States Constitution does not mandate proportionality review of death sentences).

III.

¶ 56 For the foregoing reasons, we affirm Appellant's conviction of first-degree premeditated murder and death sentence.

_____________________________________ Ruth V. McGregor, Justice

CONCURRING:

_____________________________________ Thomas A. Zlaket, Chief Justice

_____________________________________ Charles E. Jones, Vice Chief Justice

_____________________________________ Stanley G. Feldman, Justice

_____________________________________ Frederick J. Martone, Justice