On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures

We consider two positive, normalized measures dA(x) and dB(x) related by the relationship dA(x)=(C/(x+D))dB(x) or by dA(x) = (C/(x^2+E))dB(x) and dB(x) is symmetric. We show that then the polynomial sequences {a_{n}(x)}, {b_{n}(x)} orthogonal with respect to these measures are related by the relationship a_{n}(x)=b_{n}(x)+{\kappa}_{n}b_{n-1}(x) or by a_{n}(x) = b_{n}(x) + {\lambda}_{n}b_{n-2}(x) for some sequences {{\kappa}_{n}} and {{\lambda}_{n}}. We present several examples illustrating this fact and also present some attempts for extensions and generalizations. We also give some universal identities involving polynomials {b_{n}(x)} and the sequence {{\kappa}_{n}} that have a form of Fourier series expansion of the Radon--Nikodym derivative of one measure with respect to the other

The Kontorovich-Lebedev transform as a map between dd-orthogonal polynomials

A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this $KL_{\alpha}$-transform over certain polynomial sequences will be under discussion, and a special attention will be given the d-orthogonal ones. For instance, the Continuous Dual Hahn polynomials appear as the $KL_{\alpha}$-transform of a 2-orthogonal sequence of Laguerre type. Finally, all the orthogonal polynomial sequences whose $KL_{\alpha}$-transform is a $d$-orthogonal sequence will be characterized: they are essencially semiclassical polynomials fulfilling particular conditions and $d$ is even. The Hermite and Laguerre polynomials are the classical solutions to this problem.Comment: 27 page

Eksistensi Nilai Moral dan Nilai Hukum dalam Sistem Hukum Nasional

Laws that benefit a community should reflect the moral and legal values ​​of the society in which a law enforced. Likewise with the Indonesian national legal system should reflect the moral and legal values ​​contained in Pancasila. The low legal authority in to day\u27s society due to national legal systems have not fully reflect the value of moral and legal values ​​based on Pancasila. Problems in this paper is why the moral and legal values ​​of Pancasila has not been fully reflected in the current National Legal Systems. The results of the study that cause: (1) Pancasila translated in accordance with the interests of the ruler, (2) national legal reform is deadlocked due to, among others: the struggle of political interests, target orientation, ego-sectoral, bond romanticism of the past, dealing with inferiority superiority. Advice to immediately reorient and reevaluation national legal system based on Pancasila

An integral representation for the Bessel form

AbstractWe deal with integral representation problems of the Bessel form. Suitable formulations are obtained, but they are not proved for all values of the parameter. Generalizations to modified classical forms are possible

The semiclassical--Sobolev orthogonal polynomials: a general approach

We say that the polynomial sequence $(Q^{(\lambda)}_n)$ is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product $$_S= +\lambda <{{\bf u}}, {{\mathscr D}p \,{\mathscr D}r}>,$$ where ${\bf u}$ is a semiclassical linear functional, ${\mathscr D}$ is the differential, the difference or the $q$--difference operator, and $\lambda$ is a positive constant. In this paper we get algebraic and differential/difference properties for such polynomials as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional $\bf u$. The main goal of this article is to give a general approach to the study of the polynomials orthogonal with respect to the above nonstandard inner product regardless of the type of operator ${\mathscr D}$ considered. Finally, we illustrate our results by applying them to some known families of Sobolev orthogonal polynomials as well as to some new ones introduced in this paper for the first time.Comment: 23 pages, special issue dedicated to Professor Guillermo Lopez lagomasino on the occasion of his 60th birthday, accepted in Journal of Approximation Theor

Problematic Dilemma of The Limitation of Granting Remission for Corruption Prisoners

Corruption is an extraordinary crime, so the law enforcement for corruption cases must also be done extraordinarily. Therefore, the corruption prisoners or corruptors should be differentiated by their pattern of guidance in Penitentiary. The difference in the process of fostering in Penitentiary is in the form of limitation of granting remission for corruptors. The existence of such restrictive policy poses a problem dilemma to the guidance of current corruption prisoners based on Penitentiary System. This is because the penitentiary system essentially sees the crime of "deprivation of liberty" against a person is only "temporary" so that there is a reduction in criminal or remission for every prisoner. The problem is how to overcome the dilemma of granting remission for corruptors in the perspective of the correctional system. The research method is normative juridical with the regulation of law and doctrinal approach. The result of this research is to overcome the dilemma of granting remission for corruptors by revising Government Regulation Number 99 of 2012 on Terms and Procedures Implementation of Rights of Citizens Correctional Penitentiary that distinguishes the requirements for corruption prisoners that cause losses of state in the high or low nominal. For the corruption prisoners that doing corruption in the high nominal to get the special requirement for granting remission should be added in the high profile corruption prisoners are required to accomplish morality education on the nation and homeland patriotism at their expenses. While the lower profile ones are required to following the common standard coaching for general prisoners. Keywords: Remissions, Corruption Prisoners, Corruption, Correctional Syste

Restorative Justice for Users of Narcotics Through Implementation of Depenalization

Restorative Justice is a policy that puts a focus on recovery rather than retaliation. The Restorative Justice implementation, considered more effective in terms of Justice and effectiveness, makes the Restorative Justice policy renewal of the criminal law system in Indonesia. The writing of this article uses a descriptive-analytical research method that prioritizes a normative juridical approach, with the formulation of the problem regarding the role of Restorative Justice as an effort to reform criminal law and the implementation of Restorative Justice as an alternative step in law enforcement for narcotics crimes. The result of this article is that the policy regarding Restorative Justice in its application is an update in law, especially criminal law. Conventional Justice Policies which are considered ineffective in their application are now being updated through the Restorative Justice policy; in addition to the context of the application, which is not only applied within the scope of general criminal law, in Narcotics crimes, a criminal settlement mechanism is also applied using Restorative Justice policies as stated in the Circular Letter of the Supreme Court Number 4 of 2010 concerning Placement of Abuse, Victims of Abuse and Narcotics Addicts into Medical and Social Rehabilitation Institutions (SEMA.4/2010). Rehabilitation of a Narcotics defendant can be carried out if it meets the requirements described in the regulation

An integral representation for the Bessel form

AbstractWe deal with integral representation problems of the Bessel form. Suitable formulations are obtained, but they are not proved for all values of the parameter. Generalizations to modified classical forms are possible