Derivation of the Optimal Solution for the Economic Production Quantity Model with Planned Shortages without Derivatives

In this paper, we study a reformulation of the Economic Production Quantity (EPQ) problem. We study a more general version of the problem first and derive the conditions for an optimal solution, as well as the optimal solution itself, all without using derivatives. Then, we apply the approach to the reformulated EPQ problem. This version of the EPQ problem has been tackled by a number of researchers, wherein they have derived the conditions for the optimal solution and proposed algebraic derivations. However, their derivations for the conditions, as well as the optimal solution, have been shown to be questionable. Other than being questionable, the existing approaches are so complicated that they defeat the purpose of simplifying the optimization by using a derivative-free approach. We propose a correct and more succinct, much less complicated approach to derive the conditions and the optimal solution without using derivatives.

A Result on Convergence of Sequences of Iterations with Applications to Best-Response Dynamics

The result that says the sequence of iterations [Formula: see text] converges if [Formula: see text] is an increasing function has numerous applications in elementary economic analysis. I generalize this simple result to some mappings [Formula: see text]. The applications of the new result include the convergence of the best-response dynamics in the general version of the Crawford and Sobel model and in some versions of the Hotelling and Tiebout models.

On the Irreducible Factors of a Polynomial and Applications to Extensions of Absolute Values

Polynomial factorization over a field is very useful in algebraic number theory, in extensions of valuations, etc. For valued field extensions, the determination of irreducible polynomials was the focus of interest of many authors. In 1850, Eisenstein gave one of the most popular criterion to decide on irreducibility of a polynomial over Q. A criterion which was generalized in 1906 by Dumas. In 2008, R. Brown gave what is known to be the most general version of Eisenstein-Schönemann irreducibility criterion. Thanks to MacLane theory, key polynomials play a key role to extend absolute values. In this chapter, we give a sufficient condition on any monic plynomial to be a key polynomial of an absolute value, an irreducibly criterion will be given, and for any simple algebraic extension L=Kα, we give a method to describe all absolute values of L extending ∣∣, where K is a discrete rank one valued field.

Series with Commuting Terms in Topologized Semigroups

We show that the following general version of the Riemann–Dirichlet theorem is true: if every rearrangement of a series with pairwise commuting terms in a Hausdorff topologized semigroup converges, then its sum range is a singleton.

Mapping of the GEVA Items to the ICF: Preliminary Results Based on the Content of a Tool Guide Used to Assess the Needs of Persons With Disabilities in France

The aim of this research is two-fold. Firstly, mapping the GEVA items on to the ICF will allow identifying those items that are covered by the ICF and assist in improving the data collection process. Secondly this work will provide a first exploration of the items that are not covered by the ICF and that could lead to potential proposals for updating the ICF. The preliminary results show that the items of the GEVA 2008 general version are partly covered by the ICF 2017 Browser version categories. In every section of the GEVA, some of the items might be coded with ICF codes coming from the following ICF components: Body functions, Activities and Participation, Environmental factors, Personal factors. The items of the section 6 remains those mostly covered by the ICF. Throughout the GEVA, many environmental factors are documented. Although further analysis is needed to better inform the use of qualifiers (performance, capacity, satisfaction) together with the activities and the environmental factors, the identified ICF codes could assist in improving the data collection process. Finally, some items might be discussed to become potential ICF updates proposals.

Book Review: Filsafat Ilmu: Menelusuri Jejak Integrasi Filsafat, Sains, dan Sufisme (The Philosophy of Science: Tracking the Integration of Philosophy, Science, and Sufism

The book entitled "Filsafat Ilmu: Menelurusi Jejak Integrasi Filsafat, Sains, dan Sufisme (Philosophy of Science: Tracing the Paths of Integration of Philosophy, Science and Sufism)" has a total page of 192 pages with very dense and concise content in both language and weight. This book was written by Dr. Asep Salahudin, who is vice-chancellor of IAILM Suryalaya academic years 2016-2020, chairman of West Java PWNU Lakpesdam 2017-2021, lecturer at FIS Unpad and Postgraduate UIN Bandung, and Expert Staff of the Presidential Work Unit for Pancasila Ideology Development 2017-2018. He also received many awards and written works, with one of the recently published books being this book itself. The book written by Asep Salahudin has ten chapters, most of which contain philosophy from an Islamic point of view, while the rest are explanations of philosophy in general. Thus, the author divides into two parts of ten chapters, namely the first five chapters contain a description of philosophy in general which consists of chapters 1, 2, 3, 5, and 6, while the last five chapters are chapters 4, 7, 8, 9, and 10 contains about philosophy from an Islamic perspective applied by previous Islamic philosophers. The purpose of writing this book is to answer matters related to knowledge requirements to become science and to make Islamic philosophy revive in today's modern era, as it was at the peak of its previous glory. As a result of this goal, the book written by Asep Salahudin discusses the general version of the philosophy of science and the Islamic version of the philosophy of science. This general version of the philosophy of science explains the general picture of philosophy itself, including the history of its development altogether. In contrast, this Islamic version of the philosophy of science explains philosophy from the perspective of Islamic philosophers, including criticizing western philosophical thought. Therefore, the purpose of writing this book is to describe the general version of the philosophy of science and Islam, which aims to make Islamic philosophy return to its previous heyday.

Wavelet field decomposition and UV ‘opaqueness’

A large body of work over several decades indicates that, in the presence of gravitational interactions, there is loss of localization resolution within a fundamental (∼ Planck) length scale ℓ. We develop a general formalism based on wavelet decomposition of fields that takes this UV ‘opaqueness’ into account in a natural and mathematically well-defined manner. This is done by requiring fields in a local Lagrangian to be expandable in only the scaling parts of a (complete or, in a more general version, partial) wavelet Multi-Resolution Analysis. This delocalizes the interactions, now mediated through the opaque regions, inside which they are rapidly decaying. The opaque regions themselves are capable of discrete excitations of ∼ 1/ℓ spacing. The resulting effective Feynman rules, which give UV regulated and (perturbatively) unitary physical amplitudes, resemble those of string field theory.

On the Computation of Some Topological Descriptors to Find Closed Formulas for Certain Chemical Graphs

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.

On Certain Aspects of Topological Indices

A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.