Sufficient Conditions Research Articles

Posterior properties with censored responses using the gamma distribution

This research investigates the properties of the posterior distribution of the gamma distribution, especially in the context of right-censored data. We establish necessary and sufficient conditions for determining when improper priors lead to proper posteriors. Additionally, we derive conditions to ascertain the finiteness of the posterior moments. The study addresses the challenges posed by censoring and delves into the application of various objective priors. We introduce a novel estimator for censored data, enhancing the efficiency of the Markov Chain Monte Carlo (MCMC) algorithm. Through a simulation study, we evaluate the performance of Bayesian estimators under different priors. Our methodology is applied to a dataset from the Cancer Genome Atlas, focussing on lung adenocarcinoma in patients over 70, offering valuable insights into disease progression and mortality patterns.

Controllability of stochastic semilinear systems

In this paper, we demonstrate that the exact controllability concept is inappropriate for stochastic systems by proving the nonfulfillment of the coercivity inequality. As a result, we explore the concept of C-controllability, which was introduced as a weaker alternative to exact controllability when the controllability problem was first extended to stochastic systems. We establish a sufficient condition for C-controllability in finite-dimensional semilinear stochastic systems driven by a Wiener process and illustrate the result with several examples.

Coincidence of the nth class-preserving and subcentral automorphism groups of finite p-groups

Let G be a group. An automorphism α of G is called an n th class-preserving automorphism if for all g ∈ G , we have α ( g ) ∈ g γ n ( G ) . The set Aut c n ( G ) of all nth class-preserving automorphisms of G forms a normal subgroup of Aut ( G ) . For a normal subgroup X of G, let Aut X ( G ) denote the subgroup of Aut ( G ) centralizing G / X . In this paper, we give necessary and sufficient conditions for a finite non-abelian p-group G of class n + 1 to satisfy Aut c n ( G ) = Aut H ( G ) , where 1 ≠ H ≤ Z ( G ) , and obtain the main results of Shabani-Attar and Garg as particular cases.

Analyzing the Synergistic Effects of Population and Pollution on Forest Resources: A Mathematical Model

The alteration in concentration of atmospheric pollutants is influencing the functionality and growth of forests. Also, the growing human demand for forestry resources is detrimentally affecting the sustainability of these valuable resources. In this study, we present a mathematical model that incorporates the influence of atmospheric pollutants on the intrinsic growth rate of forests, while concurrently addressing the utilization of forestry land by the human population for diverse purposes which diminishes the carrying capacity of forestry resources. We establish sufficient conditions under which all relevant dynamic variables stabilize at their equilibria. Upon scrutinizing the model system, we observe multiple bifurcations concerning certain key parameters. Additionally, numerical simulations have been conducted to corroborate the analytically derived findings. Moreover, we fortify the proposed model through the integration of a time delay in the impact of pollutants on the intrinsic growth rate of forestry resources. Despite the conventional belief that introducing a time delay tends to destabilize systems, our resolute delayed model system showcases that a time delay in the effect of pollutants on intrinsic growth rate of forestry resources can, in fact, stabilize the unstable interior equilibrium.

Gadget Construction and Structural Convergence

Nešetřil and Ossona de Mendez recently proposed a new definition of graph convergence called structural convergence. The structural convergence framework is based on the probability of satisfaction of logical formulas from a fixed fragment of first-order formulas. The flexibility of choosing the fragment allows to unify the classical notions of convergence for sparse and dense graphs. Since the field is relatively young, the range of examples of convergent sequences is limited and only a few methods of construction are known. Our aim is to extend the variety of constructions by considering the gadget construction. We show that, when restricting to the set of sentences, the application of gadget construction on elementarily convergent sequences yields an elementarily convergent sequence. On the other hand, we show counterexamples witnessing that a generalization to the full first-order convergence is not possible without additional assumptions. We give several different sufficient conditions to ensure the full convergence. One of them states that the resulting sequence is first-order convergent if the replaced edges are dense in the original sequence of structures.

Enhancing the transformative potential of sustainability innovations: An application of the values-rules-knowledge framework.

To respond to global sustainability challenges with transformative solutions, there is a need to pinpoint the necessary and sufficient conditions that enhance the transformative potential of sustainability innovations. To this end, we examined 129 sustainability innovations in two European Biosphere Reserves, and analysed (1) their transformative potential, assessed based on a leverage points perspective, and (2) their supportive conditions (i.e. decision contexts, or constellations of values, rules and knowledge). Specifically, we used social network analyses to characterise different rules, or governance arrangements in the two Biosphere Reserves. By comparing the decision contexts of transformative and incremental innovations, we provide empirical evidence that plural values, coproduction and networks that are diverse, collaborative and influential, enable transformative innovations. Shallow leverage points seem insufficient but necessary to operationalise transformative change. Future research should explore the co-evolution of decision contexts and transformative potential, to better understand how to shift incremental to transformative innovations.

Distributed H ∞ moving horizon estimation over energy harvesting sensor networks

This paper addresses the distributed H ∞ moving horizon estimation problem for nonlinear systems over energy harvesting sensor networks in a deterministic framework, where each sensor is able to gather energy from the surrounding environment. A transformed Poisson process model is introduced to describe the energy collected by each sensor, with particular consideration given to the minimum energy collected. In contrast to previous research on distributed state estimation over energy harvesting sensor networks, which solely considered the energy costs associated with transmission and assumed knowledge of the statistical properties of harvested energy, we consider a more comprehensive scenario. Specifically, we account for the energy costs associated with both sensor sensing and data transmission to neighbouring sensors, while only the parameters of the minimum harvested energy are known. Subsequently, a novel energy allocation strategy is proposed to provide energy for each sensor sensing and transmission based on a predetermined fixed circular order, which determines a maximum time interval for each sensor sensing and transmission. Then, local measurement output predictors and prior state predictors are constructed to handle interruptions in sensor sensing and communication caused by the energy harvesting mechanism. Furthermore, we derive sufficient conditions for the existence of a distributed moving horizon estimator, ensuring H ∞ consensus. To illustrate the proposed method's effectiveness, a single-machine infinite-bus power system is presented.

The second-order zero differential spectra of some APN and other maps over finite fields

The Feistel Boomerang Connectivity Table and the related notion of [Formula: see text]-Boomerang uniformity (also known as the second-order zero differential uniformity) have been recently introduced by [H. Boukerrou, P. Huynh, V. Lallemand, B. Mandal and M. Minier, On the Feistel counterpart of the boomerang connectivity table, IACR Trans. Symmetric Cryptol. 1 (2020) 331–362]. In the same paper, a characterization of almost perfect nonlinear (APN) functions over fields of even characteristic in terms of second-order zero differential uniformity was also given. Here, we find a sufficient condition for an odd or even function over fields of odd characteristic to be an APN function, in terms of second-order zero differential uniformity. Moreover, we compute the second-order zero differential spectra of several APN or other low differential uniform functions, and show that our considered functions also have low second-order zero differential uniformity, though it may vary widely, unlike the case for even characteristic, when it is always zero.

Products of functions with bounded Hess+ complement

We denote by Hess + ( f ) the set of all points p ∈ R n for which the Hessian matrix H p ( f ) of the C 2 -smooth function f : R n ⟶ R is positive definite. In this paper we provide some sufficient conditions on two functions f , g : R n ⟶ R with bounded Hess + complements such that their product fg has bounded Hess + complement as well.

New additive properties of EP elements in a ring with involution

We present new necessary and sufficient condition under which the sum of two EP elements in a *-ring has core inverse. As an application, we establish certain conditions under which a block complex with EP subblocks has core inverse.

Regular immersions directed by algebraically elliptic cones

Abstract Let 𝑀 be an open Riemann surface and 𝐴 the punctured cone in C n ∖ { 0 } \mathbb{C}^{n}\setminus\{0\} on a smooth projective variety 𝑌 in P n − 1 \mathbb{P}^{n-1} . Recently, Runge approximation theorems with interpolation for holomorphic immersions M → C n M\to\mathbb{C}^{n} , directed by 𝐴, have been proved under the assumption that 𝐴 is an Oka manifold. We prove analogous results in the algebraic setting, for regular immersions directed by 𝐴 from a smooth affine curve 𝑀 into C n \mathbb{C}^{n} . The Oka property is naturally replaced by the stronger assumption that 𝐴 is algebraically elliptic, which it is if 𝑌 is uniformly rational. Under this assumption, a homotopy-theoretic necessary and sufficient condition for approximation and interpolation emerges. We show that this condition is satisfied in many cases of interest.

Mutually asymptotic Fekete sequences

Abstract A sequence of point configurations on a compact complex manifold is asymptotically Fekete if it is close to maximizing a sequence of Vandermonde determinants. These Vandermonde determinants are defined by tensor powers of a Hermitian ample line bundle and the point configurations in the sequence possess good sampling properties with respect to sections of the line bundle. In this paper, given a collection of Hermitian ample line bundles, we address the question of existence of a sequence of point configurations which is asymptotically Fekete with respect to each of the line bundles. We give a conjectural necessary and sufficient condition and prove this in the toric case.

A method in non-destructive testing for lead shielding exceeding 25 kg/m2 using 18F.

Non-Destructive Testing (NDT) is a commonly used technique for barrier verification within radiation protection, ensuring compliance with national standards and state regulations. There are currently limited published methods in NDT for lead shielding above 25 kg/m2, and thus this research aimed to develop a reproducible method to aid in 'in the field' NDT for lead barriers exceeding 25 kg/m2 using a Fluorine-18 (18F) source. Due to the fast decay of 18F, the data generated within this research was compiled from Monte Carlo (MC) simulations using the PENELOPE engine, and the PENGEOM geometry system to model the proposed empirical setup. The model predicted the Transmission Factor (TF) through area densities (thickness) of lead attenuators up to 302.7 kg/m2, with results validated by empirical measurements using a Source-to-Detector Distance (SDD) of 38.1 ± 0.05 cm and 52.7 ± 0.05 cm. However, the study was limited by the chosen activity of 18F at approximately 180 MBq, where the simulated TF curves demonstrated correspondence of data up to and including area densities of 162.4 kg/m2 using a 38.1 ± 0.05 cm SDD, and 138.0 kg/m2 with a 52.7 ± 0.05 cm SDD. Beyond these thicknesses, the empirical transmission curves deviated from simulated curves due to measurable transmissions becoming significantly reduced. This research demonstrated that using SDDs above 23 cm would provide sufficient near narrow beam conditions with the proposed experimental configuration for in-the-field NDT. The research aimed to develop an equation and method for NDT using a 18F source for lead barriers greater than 25 kg/m2, with transmission data to be made available upon request to the author.

Necessary and Sufficient Design Conditions for Overconstrained Cam Mechanisms With Flat-Faced and Roller Follower

Abstract Cam, a mechanism usually used to transform a rotary motion into the desired output motion, has been commonly used in the modern industry. In practice, various practical methods have been discussed to analyze and synthesize the cam mechanism. However, the mobility of the cam mechanism is seldom mathematically addressed. This article mathematically discusses the necessary and sufficient design conditions for four kinds of overconstrained cam mechanisms (the one with a translating flat-faced follower, a translating roller follower, an oscillating flat-faced follower, and an oscillating roller follower) to be mobile. For the first two overconstrained cam mechanisms, the relation between the design conditions and the mobility of the cam mechanism is derived by proving that the identical cam contour can be enveloped by the top and bottom follower faces. For the third overconstrained cam mechanism, the relation is derived by transforming the cam contour into a geometric layout associated with an orthoptic curve. For the fourth overconstrained cam mechanism, it is shown that the cam mechanism cannot be theoretically designed due to the variable length of the follower's arm, which does not obey the rigid body assumption. In conclusion, by means of these geometric methods, the first three kinds of cam mechanisms are proved to be mobile if and only if they satisfy the design conditions, and the last cam mechanism is proved to be theoretically infeasible.

Explicit Form of Solutions of Second-Order Delayed Difference Equations: Application to Iterative Learning Control

A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. The closed form of its solution is derived by means of a newly defined delayed matrix sine/cosine using the Z transform and determining function. This representation helps with analyzing iterative learning control by applying appropriate updating laws and ensuring sufficient conditions for achieving asymptotic convergence in tracking.

A Sufficient Condition for Second-order Differential Subordination of Harmonic Mappings

A Sufficient Condition for Second-order Differential Subordination of Harmonic Mappings

ON IDENTITIES OF REES QUOTIENTS OF FREE INVERSE SEMIGROUPS DEFINED BY POSITIVE RELATORS

Abstract We give a complete description of Rees quotients of free inverse semigroups given by positive relators that satisfy nontrivial identities, including identities in signature with involution. They are finitely presented in the class of all inverse semigroups. Those that satisfy a nontrivial semigroup identity have polynomial growth and can be given by an irredundant presentation with at most four relators. Those that satisfy a nontrivial identity in signature with involution, but which do not satisfy a nontrivial semigroup identity, have exponential growth and fall within two infinite families of finite presentations with two generators. The first family involves an unbounded number of relators and the other involves presentations with at most four relators of unbounded length. We give a new sufficient condition for which a finite set X of reduced words over an alphabet $A\cup A^{-1}$ freely generates a free inverse subsemigroup of $FI_A$ and use it in our proofs.

Performance Analysis of a Hexagon Rolling Mechanism With Single Degree of Freedom

Abstract This article presents a comprehensive performance analysis of the step-climbing and passive rolling modes of a hexagon rolling mechanism with single-degree-of-freedom, based on its structural characteristics and the constraints of centroid stability. First, a step-climbing model, incorporating motion parameters and support distance parameters, is established by leveraging the symmetrical posture movement characteristics of the hexagon rolling mechanism. Building on this foundation, the impact of each parameter on the mechanism's step-climbing ability is thoroughly analyzed, and the maximum height achievable during step climbing is also examined. Subsequently, the existence and sufficient conditions for the hexagon rolling mechanism to achieve passive rolling are analyzed using the centroid fluctuation curve and its slope curves. The analysis results indicate that, due to its unique coupling structure design, the hexagon rolling mechanism possesses a passive rolling capability that is not available in conventional planar linkage mechanisms. Finally, the correctness of the theoretical model is validated through both simulation and prototype experiments.

Irreducible tensor product modules over the W-algebra W(2,2)

In this paper, we construct a class of non-weight modules [Formula: see text] over the [Formula: see text]-algebra [Formula: see text] by taking tensor products of modules [Formula: see text] with restricted modules [Formula: see text]. Then, we give the necessary and sufficient conditions for the irreducibility of such tensor product modules and determine the conditions under which two irreducible tensor product modules are isomorphic. These non-weight modules are different from known non-weight modules. Finally, we transform some tensor product modules into induced modules from modules of certain subalgebras over the [Formula: see text]-algebra [Formula: see text]. And the conditions for these induced modules to be irreducible are determined by applying the established results.

On integrable deformations of the Cherednik model

In this paper, we provide the [Formula: see text]-model formulation of the non-deformed Cherednik model as well as of its Poisson-Lie and Poisson-Lie-WZ deformed version. In all three cases, we solve the sufficient condition of integrability by using the [Formula: see text]-model formalism. We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.