Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.

ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY

A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.

ε-super Effcient Solutions of Optimization Problems with Set-valued Maps in Locally Convex Space

In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.

Generalized cone-subconvexlike set-valued maps and applications to vector optimization

The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

An Improvement of Existence Theorems of Additive Selection Maps for Sub-additive Set-valued Maps

In this paper, we will construct a new class of subadditive set-valued maps and use Cantor theorem to prove that the set-valued map has an unique additive selection map when the set-valued map satisfies some certain conditions, and then compare the obtained result with the well-known results.

Topological Stability and Entropy for Certain Set-valued Maps

In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is given.Furthermore,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.

Optimality Conditions of the Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps Characterized by Contingent Epiderivative

In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.

EXISTENCE PROBLEMS OF ADDITIVE SELECTION MAPS FOR ANOTHER TYPE SUBADDITIVE SET-VALUED MAP

In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set-valued map.

The Unique Existence of Additive Selection Maps for a Weak Subadditive Set-valued Map

In this paper, we discuss the unique existent problems of a additive selection map for the following map F:X→P0(Y):F(r∑i=1αixi)■r∑i=1αiF(xi),■xi∈K,i=1, ··· , r,where αi and αi (i = 1, ··· , r) are all non-negative real numbers.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Common Fixed Point Theorems for Sequences of φ-type Contraction Set-valued Mappings

In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.

Oruxmaps软件结合Global Mapper软件在矿产资源行业并购中的应用

纸质地质图结合手持GPS,采用手工方式野外记录的传统地质调查工作方式已不能适应数字化和信息化的要求,在矿产资源并购项目中,运用Oruxmaps、Global Mapper等软件,可以制作适应地质调查工作所特需的离线地质图,实现地质图、GPS定位、路线轨迹记录、文字记录、影像记录等的有机结合,形成了一套行之有效的工作流程,极大地提高了路线地质调查工作的质量和效率。

VALUE DISTRIBUTION PROPERTIES FOR GAUSS MAPS OF IMMERSED HARMONIC SURFACES RAMIFIED OVER HYPERSURFACES

In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a family of hypersurfaces{Q_(j)}_(j=1)^(q)in P^(m-1)(C)located in the N-subgeneral position.In addition,we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in R^(3)whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.

Leveraging ROTI map derived from Indonesian GNSS receiver network for advancing study of Equatorial Plasma Bubble in Southeast/East Asia

This paper highlights the crucial role of Indonesia’s GNSS receiver network in advancing Equatorial Plasma Bubble(EPB)studies in Southeast and East Asia,as ionospheric irregularities within EPB can disrupt GNSS signals and degrade positioning accuracy.Managed by the Indonesian Geospatial Information Agency(BIG),the Indonesia Continuously Operating Reference Station(Ina-CORS)network comprises over 300 GNSS receivers spanning equatorial to southern low-latitude regions.Ina-CORS is uniquely situated to monitor EPB generation,zonal drift,and dissipation across Southeast Asia.We provide a practical tool for EPB research,by sharing two-dimensional rate of Total Electron Content(TEC)change index(ROTI)derived from this network.We generate ROTI maps with a 10-minute resolution,and samples from May 2024 are publicly available for further scientific research.Two preliminary findings from the ROTI maps of Ina-CORS are noteworthy.First,the Ina-CORS ROTI maps reveal that the irregularities within a broader EPB structure persist longer,increasing the potential for these irregularities to migrate farther eastward.Second,we demonstrate that combined ROTI maps from Ina-CORS and GNSS receivers in East Asia and Australia can be used to monitor the development of ionospheric irregularities in Southeast and East Asia.We have demonstrated the combined ROTI maps to capture the development of ionospheric irregularities in the Southeast/East Asian sector during the G5 Geomagnetic Storm on May 11,2024.We observed simultaneous ionospheric irregularities in Japan and Australia,respectively propagating northwestward and southwestward,before midnight,whereas Southeast Asia’s equatorial and low-latitude regions exhibited irregularities post-midnight.By sharing ROTI maps from Indonesia and integrating them with regional GNSS networks,researchers can conduct comprehensive EPB studies,enhancing the understanding of EPB behavior across Southeast and East Asia and contributing significantly to ionospheric research.

THE EXISTENCE OF PSEUDOHARMONIC MAPS FOR SMALL HORIZONTAL ENERGY

In this paper,we consider pseudoharmonic heat flow with small initial horizontal energy and give the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds into closed Riemannian manifolds.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Formal Concept Analysis Based on Set-valued Mapping

Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.

Nonadditive Skew(Anti-)commuting Maps on Operator Algebras

In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.

Whole-volume histogram analysis of spectral-computed tomography iodine maps characterizes HER2 expression in gastric cancer

BACKGROUND Although surgery remains the primary treatment for gastric cancer(GC),the identification of effective alternative treatments for individuals for whom surgery is unsuitable holds significance.HER2 overexpression occurs in approximately 15%-20%of advanced GC cases,directly affecting treatment-related decisions.Spectral-computed tomography(sCT)enables the quantification of material compositions,and sCT iodine concentration parameters have been demonstrated to be useful for the diagnosis of GC and prediction of its invasion depth,angioge-nesis,and response to systemic chemotherapy.No existing report describes the prediction of GC HER2 status through histogram analysis based on sCT iodine maps(IMs).AIM To investigate whether whole-volume histogram analysis of sCT IMs enables the prediction of the GC HER2 status.METHODS This study was performed with data from 101 patients with pathologically confirmed GC who underwent preoperative sCT examinations.Nineteen parameters were extracted via sCT IM histogram analysis:The minimum,maximum,mean,standard deviation,variance,coefficient of variation,skewness,kurtosis,entropy,percentiles(1st,5th,10th,25th,50th,75th,90th,95th,and 99th),and lesion volume.Spearman correlations of the parameters with the HER2 status and clinicopathological parameters were assessed.Receiver operating characteristic curves were used to evaluate the parameters’diagnostic performance.RESULTS Values for the histogram parameters of the maximum,mean,standard deviation,variance,entropy,and percentiles were significantly lower in the HER2+group than in the HER2–group(all P<0.05).The GC differentiation and Lauren classification correlated significantly with the HER2 status of tumor tissue(P=0.001 and 0.023,respectively).The 99th percentile had the largest area under the curve for GC HER2 status identification(0.740),with 76.2%,sensitivity,65.0%specificity,and 67.3%accuracy.All sCT IM histogram parameters correlated positively with the GC HER2 status(r=0.237-0.337,P=0.001-0.017).CONCLUSION Whole-lesion histogram parameters derived from sCT IM analysis,and especially the 99th percentile,can serve as imaging biomarkers of HER2 overexpression in GC.