Appellant, Alvin Ray Williams, appeals the judgment of the Pulaski County Circuit Court convicting him of first-degree murder and sentencing him to imprisonment for life. Jurisdiction of this appeal is properly in this court pursuant to Ark. Sup. Ct. R. l-2(a)(2). Appellant’s two points for reversal are a challenge to the sufficiency of the evidence and a constitutional challenge to our bifurcated proceedings in criminal cases. We find no merit to the arguments and affirm the judgment of conviction which was entered pursuant to a jury verdict.
I. MOTION FOR DIRECTED VERDICT
Appellant’s first point of error is the denial of his motions for directed verdict. At the close of the state’s case, appellant moved for a directed verdict on two grounds: that the evidence established appellant’s defense of justification and that the evidence was insufficient to establish his intent to purposely cause the victim’s death. After the trial court denied appellant’s motion, appellant called a single witness in his behalf. Appellant then renewed his earlier *436motion for directed verdict, which the trial court denied.
Appellant’s initial motion was sufficiently specific to apprise the trial court of the particular grounds for the motion as required by A.R.Cr.P. Rule 33.1. Appellant’s renewal motion was therefore likewise sufficient to preserve this point for appellate review. Key v. State, 325 Ark. 73, 923 S.W.2d 865 (1996). We observe that, although appellant’s abstract is flagrantly deficient because it does not include the motions for directed verdict and does not indicate in any manner that the motions were made, Moncrief v. State, 325 Ark. 173, 425 S.W.2d 776 (1996), the state cured this deficiency by including the motions in its supplemental abstract. See generally Ark. Sup. Ct. R. 4-2(b); see also Johnson v. State, 319 Ark. 3, 888 S.W.2d 661 (1994).
We recently stated oür standard of review for directed-verdict motions:
This court treats the denial of a motion for directed verdict as a challenge to the sufficiency of the evidence. The test for determining the sufficiency of the evidence is whether there is substantial evidence to support the verdict; substantial evidence must be forceful enough to compel a conclusion one way or the other beyond suspicion and conjecture. On appellate review, it is only necessary for this court to ascertain that evidence which is most favorable to appellee, and it is permissible to consider only that evidence which supports the guilty verdict.
Choate v. State, 325 Ark. 251, 254-55, 925 S.W.2d 409, 411 (1996) (quoting King v. State, 323 Ark. 671, 916 S.W.2d 732 (1996) (other citations omitted)).
Appellant admitted that he shot and killed the victim. He defended his actions on the basis that his actions were justified — that he used only such force as he reasonably believed necessary to prevent the victim from killing him. Consequently, the only issues we need determine in reviewing the evidence are whether there is substantial evidence to support a finding that appellant acted “[w]ith a purpose of causing the death of another person” as required by Ark. Code Ann. § 5-10-102(a)(2) (Repl. 1993), and whether there was substantial evidence to support a finding of justification.
*437 A. PROOF OF PURPOSE
As applied to this case, the requisite mental state is purposely causing the death of another. Section 5-10-102(a)(2); see Walker v. State, 324 Ark. 106, 918 S.W.2d 172 (1996). “A person acts purposely with respect to his conduct or a result thereof when it is his conscious object to engage in conduct of that nature or to cause such a result[.]” Ark. Code Ann. § 5-2-202(1) (Repl. 1993).
The law is well-settled that a criminal defendant’s intent or state of mind is seldom capable of proof by direct evidence and must usually be inferred from the circumstances of the crime. Williams v. State, 321 Ark. 635, 906 S.W.2d 677 (1995). The intent necessary to sustain a conviction for first-degree murder may be inferred from the type of weapon used, from the manner of its use, and the nature, extent, and location of the wounds. Walker, 324 Ark. 106, 918 S.W.2d 172.
The law is also well-setded that circumstantial evidence of a culpable mental state may constitute substantial evidence to sustain a guilty verdict. Crawford v. State, 309 Ark. 54, 827 S.W.2d 134 (1992) (citing Farris v. State, 308 Ark. 561, 826 S.W.2d 241 (1992), and Davis v. State, 251 Ark. 771, 475 S.W.2d 155 (1972)). However, in order for circumstantial evidence alone to constitute substantial evidence, it must exclude every other reasonable hypothesis consistent with innocence. Key, 325 Ark. 73, 923 S.W.2d 865. Once the evidence is determined to be sufficient to go to the jury, the question of whether the circumstantial evidence excludes any other hypothesis consistent with innocence is for the jury to decide. Id.
That appellant caused the victim’s death with a single 9mm gunshot wound to the chest is not disputed. The following circumstances established by the evidence in this case were sufficient for the jury to infer that appellant acted with the purpose of causing the victim’s death. One witness had struggled with the victim prior to the victim’s death; this witness did not see a gun on the victim, but did see appellant with a gun just prior to the killing. Another witness argued with the victim prior to the murder. She testified that she did not see the victim with a gun during their argument but later saw appellant pull a gun from his pants and try to point it at the victim’s head; she also saw the gun up in the air “and it was just going ever which way.” This witness also testified that appellant *438initiated the altercation with the victim. Another witness, who was babysitting at the house next door to where the murder occurred, testified that she saw and heard people talking loudly in the yard; she later heard gunfire and saw one person chasing the other around a parked car; she saw the person who was doing the chasing holding a gun and heard the other person say “[pjlease don’t shoot me”; she also saw the man who had the gun leave the scene. A neighbor testified that he saw someone shooting at the victim while the victim tried to duck and dodge the bullets. The neighbor stated that the shooter would pause, look under the car to locate the victim’s feet, and then rise to fire another shot. The officer who arrested appellant found him hiding under some bushes a block from the murder scene; the officer could hear appellant breathing heavily and noticed where appellant had covered himself with leaves.
In short, after using a handgun to shoot the victim while the victim was pleading for his life and dodging and ducking bullets, appellant fled from the scene and was found to be hiding from police. From these circumstances, the jury could reasonably infer that appellant acted with the purpose of causing the victim’s death. See Williams, 321 Ark. 635, 906 S.W.2d 677; see also Crauford, 309 Ark. 54, 827 S.W.2d 134. Any conflicts and inconsistencies in the evidence were for the jury to resolve as factfinder, and not for the trial court to resolve on a directed-verdict motion. Williams, 321 Ark. 635, 906 S.W.2d 677.
B. PROOF OF JUSTIFICATION
Appellant contends that the statement he gave to the police established that his actions were justified. Appellant maintains that the evidence in this case proves that the victim was the one who initiated the confrontation; that appellant believed the victim was about to kill him; and that he and the victim began wrestling, after which appellant took the gun away from the victim and killed him in self-defense. One who asserts the defense of justification of a homicide must show not only that the person killed was using deadly physical force, but that he responded with only that force which was necessary and that he could not have avoided the killing. Ark. Code Ann. § 5-2-607 (Repl. 1993); Ricketts v. State, 292 Ark. 256, 729 S.W.2d 400 (1987). The jury was instructed accordingly by the trial court and rejected appellant’s defense. This rejection is supported by the same evidence we discussed in affirming the jury’s finding that appellant acted purposefully in this case — appellant *439was the only one seen with the gun, the victim pleaded for his life, appellant continued to shoot at the victim as the victim dodged bullets, and appellant fled the scene.
Because, when we review the denial of a motion for directed verdict, we need only consider the evidence that supports the jury’s verdict without weighing it against any evidence favorable to the accused, we conclude there is substantial evidence to support the jury’s finding of appellant’s guilt. See Williams, 321 Ark. 635, 906 S.W.2d 677. Accordingly, the trial court did not err in denying the motion for directed verdict.
II. CONSTITUTIONAL CHALLENGE TO ACT 535 OF 1993
Appellant filed a pretrial motion challenging as unconstitutional on both state and federal grounds Act 535 of 1993, codified at Arkansas Code Annotated §§ 16-97-101 to -104 (Supp. 1995), which provides for bifurcated proceedings of the determinations of guilt and punishment in felony cases. The trial court denied this motion in an omnibus hearing. Appellant’s motion included nine arguments, all of which are argued on appeal and none of which has merit. Accordingly, we conclude the trial court did not err in denying appellant’s motion.
We do not reach the merits of many of these arguments because they are all essentially one-sentence assertions with no citation to supporting authority and without explanation as to how the cited portions of the constitutions have been violated. We do not consider an argument, even a constitutional one, when the appellant presents no citation to authority or convincing argument in its support, and it is not apparent without further research that the argument is well-taken. Roberts v. State, 324 Ark. 68, 919 S.W.2d 192 (1996). This rule is consistent with the well-established principle that statutes are presumed to be constitutional and the burden of proving otherwise rests with the party challenging the statute. Id. When an appellant does not explain how a particular statute offends his constitutional rights, we do not consider his deficient contentions. Id.
*440 A. ABSENCE OF APPELLATE REVIEW OF SENTENCING
Appellant contends that the Act violates the Eighth Amendment to the United States Constitution, made applicable to the states through the Fourteenth Amendment, and Article 2, Section 9 of the Arkansas Constitution because it does not provide for appellate review of the sentence ultimately imposed. Appellant argues that the absence of appellate review of a sentence contravenes the ban on cruel and unusual punishment.
Appellant’s argument is entirely without merit as it is based upon a false premise. The Act does not prohibit or interfere with our practice of reviewing sentencing proceedings when sentencing issues are properly presented. Indeed, as the state points out, we have recently reversed a case for evidential errors that occurred in the sentencing phase. Rush v. State, 324 Ark. 147, 919 S.W.2d 933 (1996). As for review of the ultimately imposed sentence, we do not usually review the length of a sentence that is within legal limits except in limited circumstances not relevant here. Henderson v. State, 322 Ark. 402, 910 S.W.2d 656 (1995). Finally, we note that appellant makes no contention whatsoever that his sentence is erroneous or that error occurred in the sentencing phase of his trial.
B. SUNSET PROVISION
When enacted in 1993, Act 565 contained a “sunset” provision, whereby the Act would expire on June 30, 1997. Appellant argues that the sunset provision violates the due-process and equal-protection clauses of the United States and Arkansas Constitutions. This argument is rendered moot because the sunset provision was repealed by Act 892 of 1995. This court does not address moot arguments. Johnson, 319 Ark. 3, 888 S.W.2d 661.
C. VOID FOR VAGUENESS
Citing the Fourteenth Amendment to the United States Constitution and Article 2, Sections 3 and 18 of the Arkansas Constitution, and without any explanation, appellant argues that the bifurcation process is void for vagueness, fails to give adequate notice of the proscribed conduct, and denies due process and equal protection of the laws. Appellant argues further that criminal laws are to be strictly construed.
This argument is likewise wholly without merit. First, *441the Act does not proscribe any conduct at all; rather, it provides for remedial criminal procedures. Generally, we construe procedural laws liberally to achieve their remedial objectives. Second, appellant fails to articulate any particular argument about how the Act is vague or violates his due-process and equal-protection rights. We do not address such deficient contentions, even though they are constitutional ones. Roberts, 324 Ark. 68, 919 S.W.2d 192.
D. EX POST FACTO
Appellant contends the Act violates the Ex Post Facto Clauses of the United States and Arkansas Constitutions because it applies to criminal acts that occurred before its effective date. We have previously considered this argument in the federal context and concluded it was entirely without merit. Williams v. State, 318 Ark. 846, 887 S.W.2d 530 (1994). Because our state constitution’s ex post facto clause is essentially identical to the federal clause, for the same reasoning expressed in Williams, 318 Ark. 846, 887 S.W.2d 530, we hold the Act does not violate the state ex post facto clause.
E. MODEL INSTRUCTIONS
Appellant argues his state and federal due-process and equal-protection rights were violated because the Act’s bifurcation process was made applicable before the Arkansas Model Jury Instructions for Criminal Cases was amended. Appellant does not cite any authority for this contention, nor does he make a convincing argument supporting it. Accordingly, we do not address this deficient contention. Roberts, 324 Ark. 68, 919 S.W.2d 192.
F. GUILTY PLEA
Appellant argues that the Act gives the prosecutor the ultimate decision as to whether a defendant can plead guilty and therefore violates the state and federal due-process and equal-protection clauses. This argument is based upon a false premise. It is the trial court that decides whether it will accept the defendant’s guilty plea in accordance with A.R.Cr.P. Rules 24.4 to 24.6. Moreover, a defendant does not have an absolute right to plead guilty. Numan v. State, 291 Ark. 22, 722 S.W.2d 276 (1987).
G. VICTIM-IMPACT EVIDENCE
Appellant argues that the Act is unconstitutional because it allows the admission of generic victim-impact evidence *442in violation of Payne v. Tennessee, 501 U.S. 808 (1991). We have recently discussed Payne and upheld our victim-impact statute applicable in capital cases, Ark. Code Ann. § 5-4-602(4) (Repl. 1993). Kemp v. State, 324 Ark. 178, 919 S.W.2d 943 (1996). However, appellant cites no authority, nor makes any argument that Payne applies to non-capital sentencing procedures. Accordingly, we do not address this argument. Roberts, 324 Ark. 68, 919 S.W.2d 192.
H. VOIR DIRE
Appellant argues that the Act does not allow for voir dire of potential jurors concerning whether they can consider the foil range of penalties upon conviction. Appellant contends this violates his state and federal right to a fair and impartial jury. Appellant’s argument is, however, based on an entirely false premise. The Act does not purport to restrict voir dire examination of prospective jurors.
I MISDEMEANOR CONVICTIONS
Appellant contends that the Act conflicts with the Habitual Offender Statute, Ark. Code Ann. § 5-4-501 (Supp. 1993), because the Act allows for the admission of misdemeanor convictions during the sentencing phase while the Habitual Offender Statute does not allow consideration of misdemeanors for enhanced sentencing purposes. Appellant argues that this alleged conflict renders the Act unconstitutional as violative of the state and federal due-process clauses. Appellant does not cite any authority for this contention, nor does he make a convincing argument supporting it. Accordingly, we do not address this deficient contention. Roberts, 324 Ark. 68, 919 S.W.2d 192.
In accordance with Ark. Sup. Ct. R. 4-3 (h), the record has been reviewed for adverse rulings objected to by appellant but not argued on appeal, and no such errors were found. For the aforementioned reasons, the judgment of conviction is affirmed.