Basic Inequalities Research Articles

Analysis of the Implementation of Risk-Mitigation Governance in Public Services Near Yogyakarta International Airport

The public service risk mitigation implemented by local governments in Indonesia in tackling potential risks and the impact of development on local areas is important for governance reform. This study aims to analyze the public service risk mitigation carried out by the Government of Kulon Progo Regency in the YIA area. This study is a type of qualitative research with an instrumental case study methodology. Data were collected by analyzing secondary data, as well as primary data through interviews and observations. The analysis was carried out using triangulation techniques, policy adoption, comparison, searching for data explanations and inductive reasoning, and FGDs. The study findings show that risk-mitigation governance can shape public service providers to face potential risks due to reducing negative impacts on citizens’ basic rights and inequalities in the community. The risk-mitigation governance implementation runs led by the commitment of risk-oriented-local leaders, harmonization of regulations has not integrated to local-sector- law, stakeholder involvement with engagement the participation of basic service users, the private sector, as well as university, community representatives, media, and NGOs, with a collaborative and adaptable approach. Compliance and synergy among stakeholders are the most important factors forming public service risk mitigation.

The Exponential Attractor for Partially Dissipative Lattice System of Infinite Dimension

With the wide application of fractional differential equations, the study of dynamic systems of fractional differential equations has become one of the hotspots in the past decade. The attractor theory is one of the research directions of infinite dimensional lattice dynamical system. In paper, Eden et al. Systematically introduced the exponential attractor of deterministic autonomous dynamical system, which is a compact positive invariant set with finite fractal dimension and attracting orbits at exponential rate. The exponential attractor has a finite fractal dimension. Because of the exponential attractiveness, the exponential attractor is more stable under perturbation than the global attractor. Fitzhugh Nagumo equation is a nonlinear partial equation that describes the periodic oscillation of neuronal action potential under constant current stimulation above the threshold. For Fitzhugh Nagumo system, there are many reports on attractors, but few reports on exponential attractors. In this paper, the infinite dimensional lattice Fitzhugh Nagumo system [4] is studied. The specific contents are as follows: In part 1, the background, development and research status of FitzHugh Nagumo lattice system and the main work of this paper are introduced. In part 2, the basic concepts, inequalities and lemmas required in the research of FitzHugh Nagumo lattice system are introduced. In part 3, the initial value problem of FitzHugh Nagumo lattice system is studied. For any initial value ϕ(0), there exists a unique solution ϕ(t) of system (9) and family of mapping S(t) can generate continuous operator semigroup {S(t)} t≥0 on ,. Through lemma 3.2,3.3,3.4, it can be proved that the continuous operator semigroup {S(t)} t≥0 satisfies uniform continuity and is asymptotically compact, thus proving the existence of the exponential attractor of the system.

Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property

In this paper, we develop a generalized moment method with a continuous weight function for the Smoluchowski coagulation equation in its continuous form to study the mass conservation property of this equation. We first establish some basic inequalities for the generalized moment and prove the mass conservation property under a sufficient condition on the kernel and an initial condition, utilizing these inequalities. Additionally, we provide some concrete examples of coagulation kernels that exhibit mass conservation properties and show that these kernels exhibit either polynomial or exponential growth along specific particular curves.

The convergence rate of solutions in a class of chemotaxis systems with density-dependent motility and indirect signal absorption

This paper is concerned with a chemotaxis system with density-dependent motility and indirect signal absorption. By some basic inequalities, we obtain that the convergence rate of solutions is exponential as time tends to infinity for such kind of models with l<2, which improves on a recent result in [14], where the convergence rate of solutions is algebraic.

Newton–Simpson-type inequalities via majorization

In this article, the main objective is construction of fractional Newton–Simpson-type inequalities with the concept of majorization. We established a new identity on estimates of definite integrals utilizing majorization and this identity will lead us to develop new generalized forms of prior estimates. Some basic inequalities such as Hölder’s, power-mean, and Young’s along with the Niezgoda–Jensen–Mercer inequality have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. Applications to the quadrature rule are given as well. We make links between our findings and a number of well-known discoveries in the literature.

Some basic inequalities on golden Riemannian product manifolds with constant curvatures

This article is devoted to prove the basic Chen?s inequalities for slant submanifolds in Riemannian space forms equipped with Golden structure. The equality case and some particular cases of derived inequalities are discussed.

A Comparison of the Contents of “Basic Inequalities” in Senior High School Mathematics Textbooks of Jiangsu Education Version, People’s Education Version A and Beijing Normal University Version

A Comparison of the Contents of “Basic Inequalities” in Senior High School Mathematics Textbooks of Jiangsu Education Version, People’s Education Version A and Beijing Normal University Version

On some inequalities for metallic Riemannian space forms

The metallic Riemannian space forms are the subject of this article, specifically their slant submanifolds. Several basic inequalities have been derived for these submanifolds and particular conclusions are examined.

A Bias-Reduced Solution for Multistatic Localization Using Differential Delays and Doppler Shifts

In this paper, the multistatic localization problem with unknown propagation speed is investigated using differential delays and Doppler shifts between the signals from direct and indirect paths. A series of pseudo-linear equations are formulated via the transformation of measurement models. A weighted least squares (WLS) formulation is then proposed after ignoring the second-order error terms, which can be rewritten as a non-convex optimization problem with the relationships among variables included as constraints. To deal with the non-convexity of the problem, semidefinite relaxation is applied, resulting in a convex semidefinite program (SDP). Several reasonable second-order cone constraints constructed via basic inequality and Cauchy-Schwarz inequality are added to tighten the relaxed SDP problem. By preserving the second-order error terms in equations, the bias of the estimate from the WLS formulation is also derived and then subtracted to nearly eliminate the bias and reach a bias-reduced solution. Simulation results show that the mean square error (MSE) of the proposed method approaches the Cramer-Rao lower bound (CRLB) and the bias is reduced significantly.

Compulsory Basic Education and Social Inequality: State of Local Government and Compulsory and Free Education Act 2075 BS

This article analyses the constitutional and legal provisions for school education and particularly Compulsory and Free Education Act, 2075 of Nepal. These provisions are oriented toward creating an environment where all citizens can get basic education so as to enhance equal and just Society. Compulsory and Free Education Act, 2075 is enacted to implement the constitutionally Assured fundamental right to education, and provision of free and compulsory school education without evidence-based analysis, planning and budgeting. The provisions of Compulsory and Free Education Act, 2075,in essence, are closed to the imposed social order from the top envisioned by Durkheim, influence and control of the powerful section of the society by Weber and inequality in the society due to unequal access to education by the classical Marxists.

Some Basic Inequalities on (ϵ)-Para Sasakian Manifold

We propose fundamental inequalities for contact pseudo-slant submanifolds of (ϵ)-para Sasakian space form employing generalized normalized δ-Casorati curvature. We characterize submanifolds for which equality cases hold and illustrate the main result with some applications. Further, we have considered a certain type of submanifold for a Ricci soliton and after computing its scalar curvature, developed an inequality to find correlations between intrinsic or extrinsic invariants.

Syarat Cukup Ketaksamaan Holder di Ruang Lebesgue dengan Variabel Eksponen

Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.

Syarat Cukup Ketaksamaan Holder di Ruang Lebesgue dengan Variabel Eksponen

Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.

Optimal Inequalities for Hemi-Slant Riemannian Submersions

In the present paper, we establish some basic inequalities involving the Ricci and scalar curvature of the vertical and the horizontal distributions for hemi-slant submersions having the total space a complex space form. We also discuss the equality case of the obtained inequalities and provide illustrative examples.

New Estimates for Hermite-Hadamard Inequality in Quantum Calculus via (α, m) Convexity

This study provokes the existence of quantum Hermite-Hadamard inequalities under the concept of q-integral. We analyse and illustrate a new identity for the differentiable function mappings whose second derivatives in absolute value are (α,m) convex. Some basic inequalities such as Hölder’s and Power mean have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. We make links between our findings and a number of well-known discoveries in the literature. The conclusion in this study unify and generalise previous findings on Hermite-Hadamard inequalities.

Jensen's and Cantelli's inequalities with imprecise previsions

We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving information on a single bounded random variable X, considering either convex/concave functions of X (Jensen's inequalities) or one-sided bounds such as (X≥c) or (X≤c) (Markov's and Cantelli's inequalities). As for the consistency of the relevant imprecise uncertainty measures, our analysis considers coherence as well as weaker requirements, notably 2-coherence, which proves to be often sufficient. Jensen-like inequalities are introduced, as well as a generalisation of a recent improvement to Jensen's inequality. Some of their applications are proposed: extensions of Lyapunov's inequality and inferential problems. After discussing upper and lower Markov's inequalities, Cantelli-like inequalities are proven with different degrees of consistency for the related lower/upper previsions. In the case of coherent imprecise previsions, the corresponding Cantelli's inequalities make use of Walley's lower and upper variances, generally ensuring better bounds.

Maximal order group actions on Riemann surfaces

A natural problem is to determine, for each value of the integer g ≥ 2 , the largest order of a group that acts on a Riemann surface of genus g . Let N ( g ) (respectively M ( g ) ) be the largest order of a group of automorphisms of a Riemann surface of genus g ≥ 2 preserving the orientation (respectively possibly reversing the orientation) of the surface. The basic inequalities comparing N ( g ) and M ( g ) are N ( g ) ≤ M ( g ) ≤ 2 N ( g ) . There are well-known families of extended Hurwitz groups that provide an infinite number of integers g satisfying M ( g ) = 2 N ( g ) . It is also easy to see that there are solvable groups which provide an infinite number of such examples. We prove that, perhaps surprisingly, there are an infinite number of integers g such that N ( g ) = M ( g ) . Specifically, if p is a prime satisfying p ≡ 1 (mod 6) and g = 3 p + 1 or g = 2 p + 1 , there is a group of order 24( g − 1) that acts on a surface of genus g preserving the orientation of the surface. For all such values of g larger than a fixed constant, there are no groups with order larger than 24( g − 1) that act on a surface of genus g .

Existence of global weak solutions to 2D reduced gravity two-and-a-half layer model

We study the global existence of weak solutions to a reduced gravity two-and-a-half layer model appearing in oceanic fluid dynamics in two-dimensional torus. Based on Faedo–Galerkin method and weak convergence method, we construct the global weak solutions which are renormalized in velocity variable, where the technique of renormalized solutions was introduced by Lacroix-Violet and Vasseur (2018). Besides, we prove that the renormalized solutions are weak solutions, which satisfy the basic energy inequality and Bresch–Desjardins entropy inequality, but not the Mellet–Vasseur type inequality. In the proof, we use the reduced gravity two-and-a-half layer model with drag forces and capillary term as approximate system. It should be pointed out that only when the capillary term vanishes, we prove the existence of renormalized solution to the approximation system, which is different from Lacroix-Violet and Vasseur (2018) with the quantum potential.

Basic inequalities for statistical submanifolds in Golden-like statistical manifolds

Abstract In this paper, we introduce and study Golden-like statistical manifolds. We obtain some basic inequalities for curvature invariants of statistical submanifolds in Golden-like statistical manifolds. Also, in support of our definition, we provide a couple of examples.

SET THEORY AND A MODEL OF THE MIND IN PSYCHOLOGY

AbstractWe investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consists of what the first author (A.T.) has called Mammen spaces, where a Mammen space is a triple $(U,\mathcal S,\mathcal C)$ , where U is a non-empty set (“the universe”), $\mathcal S$ is a perfect Hausdorff topology on U, and $\mathcal C\subseteq \mathcal P(U)$ together with $\mathcal S$ satisfy certain axioms.We refute a conjecture put forward by Hoffmann-Jørgensen, who conjectured that the existence of a “complete” Mammen space implies the Axiom of Choice, by showing that in the first Cohen model, in which ZF holds but AC fails, there is a complete Mammen space. We obtain this by proving that in the first Cohen model, every perfect topology can be extended to a maximal perfect topology.On the other hand, we also show that if all sets are Lebesgue measurable, or all sets are Baire measurable, then there are no complete Mammen spaces with a countable universe.Further, we investigate two new cardinal invariants $\mathfrak u_{M}$ and $\mathfrak u_{T}$ associated with complete Mammen spaces and maximal perfect topologies, and establish some basic inequalities that are provable in ZFC. Then we show $\mathfrak u_{M}=\mathfrak u_{T}=2^{\aleph _{0}}$ follows from Martin’s Axiom, and, contrastingly, we show that $\aleph _{1}=\mathfrak u_{M}=\mathfrak u_{T}&lt;2^{\aleph _{0}}=\aleph _{2}$ in the Baumgartner–Laver model.Finally, consequences for psychology are discussed.