Convex Values Research Articles

On generalized logistic equations with non-local term of feedback control type

We consider a problem of finding functions λ(x),u(x) such that −Δpu=λf(x,u,∇u)−g(x,u) in Ω and u=0 on ∂Ω, λ(x)∈F(x,u(x)) a.e. in Ω. Assume that, the single-valued functions f,g and the multi-valued function F satisfy certain growth conditions. Using the fixed point index theory for multi-valued operators with non-necessary convex values, we prove the existence of one or two nontrivial non-negative solutions of the problem.

On the Attainable Set of Iterative Differential Inclusions

ABSTRACT In this paper, we consider a first-order iterative differential inclusion. We study the existence of solutions and some topological proprieties of the attainable set, where the right hand side is an upper semi-continuous multifunction with convex values. Then, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity.

Quasianalyticity, uncertainty, and integral transforms on higher grassmannians

We investigate the support of a distribution f on the real grassmannian Grk(Rn) whose spectrum, namely its nontrivial O(n)-components, is restricted to a subset Λ of all O(n)-types. We prove that unless Λ is co-sparse, f cannot be supported at a point. We utilize this uncertainty principle to prove that if 2≤k≤n−2, then the cosine transform of a distribution on the grassmannian cannot be supported inside any single open Schubert cell Σk. The same holds for certain more general α-cosine transforms and for the Radon transform between grassmannians, and more generally for various GLn(R)-modules. These results are then applied to convex geometry and geometric tomography, where sharper versions of the Aleksandrov projection theorem, Funk section theorem, and Klain's and Schneider's injectivity theorems for convex valuations are obtained.

Affine-Periodic Boundary Value Problem for a Fractional Differential Inclusion

In the article, affine-periodic boundary value problem involving fractional derivative is considered. Existence of solutions to a Caputo-type fractional differential inclusion is researched by some fixed-point theorems and set-valued analysis theory. Specifically, we consider two cases in which the multifunction has convex values and nonconvex values, respectively.

Morphological analysis of mineral grains from different sedimentary environments using automated static image analysis

The properties of sediment grain shape provide valuable information about the transport mechanisms in different sedimentary and geomorphological environments. With the emergence of new, high-resolution analytical techniques, it has become possible to quickly examine the grain shape properties of a large number of individual mineral grains. In this study, we used automated image analysis (Malvern Morphologi G3SE-ID) to investigate mineral particles of four sediment types from different depositional environments (sand sheet (1), floodplain (2) and fluvial channel deposits (3), Pleistocene infilling material of sand wedges (4), n = 20) in the Carpathian Basin (Central Europe). Our primary objective was to identify quantitative key variables that can help objectively distinguish certain geomorphological environments located in the Carpathian Basin. In our analysis and data processing (which included techniques such as hierarchical cluster analysis, Wilks' λ, Kruskal–Wallis, multivariate analysis of variance and principal component analysis) we focused on four variables related to grain shape: circularity (form), convexity (surface texture), solidity (roundness) and elongation (form). The form of sedimentary grains depends largely on the physical properties of their source area, while the roundness depends on the energy of the transport medium and the distance of transportation. Surface texture or convexity can change in a relatively short time in a fluvial environment.The study revealed that distinguishing geomorphological environments can be achieved by analyzing the circularity, convexity and solidity parameters of the sediment grains. Based on the established grouping, the analyses carried out with hundred repetitions showed that high sensitivity circularity, convexity and solidity variables were the most effective attributes regarding Kruskal–Wallis test statistics that provided significant (p < 0.001) results between the analyzed sedimentary environments, while the elongation was not able to provide significant results between the grouped samples. Statistical analyses of the MANOVA test with hundredfold repetitions showed significant differences between the derived groups. Wilks' λ test statistics and PCA showed that convexity and high sensitivity circularity discriminate the groups. Separate analyses of aeolian and fluvial sediments have been carried out. The Kruskal–Wallis analysis of variance showed the significant differences considering all four variables, and differences were also significant in the case of the MANOVA test. Wilks' λ test statistics and PCA showed that convexity, high sensitivity circularity and solidity discriminate the groups.According to our results, the circularity parameter can provide information about the transport distance, while the solidity parameter can indicate the transport energy. The convexity parameter can serve as an indicator of both transport distance, as well as post-depositional processes. Some infilling materials underwent multiple transport processes, including high energy aqueous, wind transport mechanisms, and the post-depositional alteration process (frost weathering), while others originated from sand-sheet covered areas (active during Pleistocene glacials). The solidity parameter proved effective in separating sediments with similarly high convexity values (smooth surface), which were, in our case, from recent aeolian and fluvial environments. This result was due to the investigated fluvial sediments that inherited their form and low level of roundness from their source area. Our research supports that aeolian transport is more effective in rounding the grains than the aqueous environment.Using automated static image analysis producing statistically stable results with hundreds of analyzed mineral grains provides useful indicators for paleogeographical reconstruction studies by investigating paleo and recent sediments.

The Existence Theorems of Fractional Differential Equation and Fractional Differential Inclusion with Affine Periodic Boundary Value Conditions

This paper is devoted to investigating the existence of solutions for the fractional differential equation and fractional differential inclusion of order α∈(2,3] with affine periodic boundary value conditions. Applying the Leray–Schauder fixed point theorem, the existence of the solutions for the fractional differential equation is established. Furthermore, for the fractional differential inclusion, we consider two cases: (i) the set-valued function has convex value and (ii) the set-valued function has nonconvex value. The main tools of our research are the Leray–Schauder alternative theorem, Covita and Nadler’s fixed point theorem and some set-valued analysis theories.

The Changing Risk Preferences of High-Net-Worth Individual Investors During the Global Financial Crisis

This paper studies how high-net-worth individual (HNWI) investors changed their risk preferences during the Global Financial Crisis (from 2007 to 2009) and how their asset allocation evolved in the same period. We had access to a confidential database from a Swiss international private bank with two samples of risk preferences questionnaires (suitability tests) filled by the same HNWI investors in 2007 and 2009. We compared the suitability tests’ suggested investment profiles to those investors’ real asset allocations at the same moments in time. We estimated correlation coefficients and ran hypothesis tests to examine if the changes in risk preferences during the period were statistically significant. Findings: HNWI investors’ risk preferences changed during the period, but the gap between their self-assessed risk preference and their real asset allocation narrowed, suggesting that they have a convex value function curve. We found evidence consistent with the psychological risk-as-feelings model, as lower risk-exposed HNWI investors also tended to decrease their risk preference level during a crisis. The evidence also suggests a stronger preference for cash during the crisis period, confirming the results of studies that have focused on the importance of liquidity during external shocks.

Multipoint boundary value problems for higher-order Hadamard fractional neutral differential equations and inclusions

In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence and uniqueness of the solution of the equation by using several fixed point theorems, and we also consider the Ulam–Hyers stability of the solution. In addition, we study the differential inclusion problem with multipoint boundary value conditions and prove the existence of the solution of the boundary value problem when the multivalued map has convex values. We also give several examples to illustrate the feasibility of the results.

T-convex T-differential fields and their immediate extensions

Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring and a $T$-derivation. If this derivation is continuous with respect to the valuation topology, then we call $K$ a $T$-convex $T$-differential field. We show that every $T$-convex $T$-differential field has an immediate strict $T$-convex $T$-differential field extension which is spherically complete. In some important cases, the assumption of polynomial boundedness can be relaxed to power boundedness.

Stability for a Class of Differential Set-Valued Inverse Variational Inequalities in Finite Dimensional Spaces

In this paper, we introduce and study a new class of differential set-valued inverse variational inequalities in finite dimensional spaces. By applying a result on differential inclusions involving an upper semicontinuous set-valued mapping with closed convex values, we first prove the existence of Carathéodory weak solutions for differential set-valued inverse variational inequalities. Then, by the existence result, we establish the stability for the differential set-valued inverse variational inequality problem when the constraint set and the mapping are perturbed by two different parameters. The closedness and continuity of Carathéodory weak solutions with respect to the two different parameters are obtained.

Efficient DEM simulations of railway ballast using simple particle shapes

For complex shaped materials, computational efficiency and accuracy of DEM models are usually opposing requirements. In the literature, DEM models of railway ballast often use very complex and computationally demanding particle shapes in combination with very simple contact laws. In contrast, this study suggests efficient DEM models for railway ballast using simple particle shapes together with a contact law including more physical effects. In previous works of the authors, shape descriptors, calculated in a shape analysis of two types of ballast, were used to construct simple particle shapes (clumps of three spheres). Using such a shape in DEM simulations of compression and direct shear tests, accurate results were achieved only when the contact law included additional physical effects e.g. edge breakage. A parametrisation strategy was developed for this contact law comparing DEM simulations with the measurements. Now, all the constructed simple particle shapes are parametrised allowing to study their suitability and relating their shape descriptors to those of railway ballast. The most suitable particle shapes consist of non-overlapping spheres, thus have a high interlocking potential, and have lowest sphericity and highest convexity values. In a micromechanical analysis of the four best performing shapes, three shapes show similar behaviour on the bulk and the micro-scale, while one shape differs clearly on the micro-scale. This analysis shows, which shapes can be expected to produce similar results in DEM simulations of other tests/load cases. The presented approach is a step towards both efficient and accurate DEM modelling of railway ballast.Graphic abstract

Electromagnetic Characteristics Analysis of Quadrupole Compound Orbital Electromagnetic Launcher with Different Configurations

During the operation of the Quadrupole Compound Orbital electromagnetic launcher, the current is easy to gather in the armature and the rail contact surface. Serious turn and arc ablation can occur, causing damage to the rail and the armature and affecting the life of the launcher. To better solve the thermal ablation problem of the armature and the rail, three different configurations of the rail and the armature are established, and the current density, magnetic field distribution and electromagnetic force of the rail and the armature are compared and analyzed using the finite element method, and the effect of concave and convex values of the armature rail on current distribution and electromagnetic force is discussed. The results show that the planar armature can effectively reduce the maximum current density and mitigate thermal damage. The concave elliptical rail produces the largest electromagnetic thrust and the smallest radial electromagnetic force, and the armature is more stable during firing. The maximum current density and magnetic field strength are negatively correlated with the concave and convex values; the electromagnetic thrust applied to the concave elliptical armature is negatively correlated with the concave value, while the electromagnetic force applied to the convex elliptical armature is positively correlated with the convex value.

Nonlocal Boundary Value Problems for (k,ψ)-Hilfer Fractional Differential Equations and Inclusions

In the present research, single and multi-valued (k,ψ)-Hilfer type fractional boundary value problems of order in (1,2] involving nonlocal integral boundary conditions were studied. In the single-valued case, the Banach and Krasnosel’skiĭ fixed point theorems as well as the Leray–Schauder nonlinear alternative were used to establish the existence and uniqueness results. In the multi-valued case, when the right-hand side of the inclusion has convex values, we established an existence result via the Leray–Schauder nonlinear alternative method for multi-valued maps, while the second existence result, dealing with the non-convex valued right-hand side of the inclusion, was obtained by applying Covitz-Nadler fixed point theorem for multi-valued contractions. The obtained theoretical results are well illustrated by the numerical examples provided.

Effects of Raceway Convexity on Friction Moment of Tapered Roller Bearings

The Effects of raceway convexities on friction moment of tapered roller bearings were studied in this paper. A new theoretical model of friction torque of tapered roller bearings was established considering the roughness and convexities of inner and outer ring raceways. Friction between roller and raceways were analyzed under the condition of elastohydrodynamic lubrication. Based on the theoretical model and experiments, the changes of friction torque with respected to raceway convexities of tapered roller bearings were obtained. The results show that the friction moment decreases with the increase of raceway convexities, while the increase of raceway convexity leads to the increase of contact stress. Therefore, the convexity values should be balanced between friction torque and contact stress. The convexity values should be balanced between friction torque and contact stress. The optimum values of the bearing being measured raceway convexities should be 5 ~ 6μm under the test conditions.

Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions.

Improved PID rate control of a quadrotor with a convexity-based surrogated model

PurposeThe purpose of this paper is to develop, extend and propose an improved proportional integral derivative (PID) rate control of a quadrotor unmanned aerial vehicle based on a convexity-based surrogated firefly algorithm.Design/methodology/approachAn improved PID controller structure is proposed for the rate dynamics of the quadrotor. Optimality of the controller is ensured by a recent, simple yet efficient firefly optimization method. The hybrid structure is further enhanced with a convexity-based surrogated model function.FindingsMonte Carlo, transient response, error metrics and histogram distribution analyzes are conducted to show the performance of the proposed controller. The performance of the proposed method is evaluated under various convex combination values to further investigate the effect of the proposed surrogated model. According to the results, the proposed method is capable of controlling the rate quadrotor dynamics with the steady-state error of 0.0023 (rad/s) for P, −0.0024 (rad/s) for Q and 0 (rad/s) for the R state, respectively. Also, the least mean objective value is achieved at = 0 value of convexity in Monte Carlo trials.Originality/valueThe originality of this paper is to propose an improved PID rate controller with a convexity-based surrogated firefly algorithm.

Topological properties for a perturbed first order sweeping process

Abstract In this paper, we consider a perturbed sweeping process for a class of subsmooth moving sets. The perturbation is general and takes the form of a sum of a single-valued mapping and a set-valued mapping. In the first result, we study some topological proprieties of the attainable set, the set-valued mapping considered here is upper semi-continuous with convex values. In the second result, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. Then, we deduce a solution of the time optimality problem.

Iterative Algorithms for a System of Variational Inclusions Involving Set-Valued Quasi-Contractive Mappings in Banach Spaces

In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real Banach spaces. First, both the existence of fixed points of the set-valued quasi-contractive mappings and the solution of the system of variational inclusions are proved. Then, using the existence result, a new iterative algorithm is constructed. And then the strong convergence of the iterative sequences is proved, and the proof is novel. Finally, a numerical example is given to demonstrate the algorithm. Our results improve and extend some known results.

Ordered fields dense in their real closure and definable convex valuations

Abstract In this paper, we undertake a systematic model- and valuation-theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the language of ordered rings. In light of our results, we re-examine the Shelah–Hasson Conjecture (specialized to ordered fields) and provide an example limiting its valuation-theoretic conclusions.

Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.