Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.

A Class of Complex Quasi-Orlicz Spaces and Their Analytic RN Property

Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with continuous quasi norm and L * Φ(X) has the ARNP if and only if X does.

Evaluation of the microstructure, secondary dendrite arm spacing, and mechanical properties of Al–Si alloy castings made in sand and Fe–Cr slag molds

The microstructure and mechanical properties of as-cast A356（Al–Si） alloy castings were investigated. A356 alloy was cast into three different molds composed of sand, ferrochrome（Fe–Cr） slag, and a mixture of sand and Fe–Cr. A sodium silicate–CO_2 process was used to make the necessary molds. Cylindrical-shaped castings were prepared. Cast products with no porosity and a good surface finish were achieved in all of the molds. These castings were evaluated for their metallography, secondary dendrite arm spacing（SDAS）, and mechanical properties, including hardness, compression, tensile, and impact properties. Furthermore, the tensile and impact samples were analyzed by fractography. The results show that faster heat transfer in the Fe–Cr slag molds than in either the silica sand or mixed molds led to lower SDAS values with a refined microstructure in the products cast in Fe–Cr slag molds. Consistent and enhanced mechanical properties were observed in the slag mold products than in the castings obtained from either sand or mixed molds. The fracture surface of the slag mold castings shows a dimple fracture morphology with a transgranular fracture nature. However, the fracture surfaces of the sand mold castings display brittle fracture. In conclusion, products cast in Fe–Cr slag molds exhibit an improved surface finish and enhanced mechanical properties compared to those of products cast in sand and mixed molds.

ON VECTOR-VALUED FUNCTION SPACES WITH HELLY'S PROPERTY

If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.

A Perturbation Analysis of Low-Rank Matrix Recovery by Schatten p-Minimization

A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.

Concave Minimization for Sparse Solutions of Absolute Value Equations

Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.

Sparse recovery in probability via l_q-minimization with Weibull random matrices for 0 < q ≤ 1

Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the lrobust null space property that can weaken the D-RIP, and show that Weibull random matrices satisfy the lrobust null space property with high probability. Besides, we prove that Weibull random matrices also possess the lquotient property with high probability. Finally, with the combination of the above mentioned properties,we give two important approximation characteristics of the solutions to the l-minimization with Weibull random matrices, one is on the stability estimate when the measurement noise e ∈ R~n needs a priori ‖e‖≤ε, the other is on the robustness estimate without needing to estimate the bound of ‖e‖. The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery.

Laser Properties of Nd_2O_3 Doped Na_2O–CaO–SiO_2 Transparent Glass-Ceramics for Space Solar Energy

A series of Na20-CaO-SiO2 glass ceramics containing different content of Nd3＋ ions were prepared by the method of high temperature melting and subsequent crystallization. The absorption, excitation and emis- sion spectra of these glass ceramics were investigated; effects of Nd3＋ content and crystallization behavior on the laser properties of this material had been studied. The results show that the emission bands origi- nating from the 4F3/2 state of Nd3＋ were firstly enhanced with the increase of the Nd2O3 doping content and the crystallinity degree, and then decreased with more doping content and deepened crystalliza- tion. The possible reasons of this phenomenon were analyzed. Research will be favored to promote the development of glass ceramics laser materials for space solar energy.

Property analysis of bistatic forward-looking SAR with arbitrary geometry

Bistatic forward-looking synthetic aperture radar（SAR） has many advantages and applications owing to its twodimensional imaging capability.There could be various imaging configurations because of the geometric flexibility of bistatic platforms,resulting in kinds of models built independently among which there could be some similar even the same motion features.Comprehensive research on such systems in a more comprehensive and general point of view is required to address their difference and consistency.Property analysis of bistatic forwardlooking SAR with arbitrary geometry is achieved including stripmap and spotlight modes on airborne platform,missile-borne platform,and hybrid platform of both.Emphasis is placed on azimuth space variance of some key parameters significantly affecting the subsequent imaging processing,based on which the frequency spectra are further described and compared considering respective features of different platforms for frequency imaging algorithm developing.Simulation results confirm the effectiveness and correctness of our analysis.

The Coarse l^(p)-Novikov Conjecture and Banach Spaces with Property(H)

In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property(H).

Modulation space estimates for damped fractional wave equation

Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.

Pointwise multipliers for Besov spaces of dominating mixed smoothness-Ⅱ

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).

Asymptotically Isometric Copy of l~β(0<β<1) in Spacesof Bounded Linear Operators

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.

Equivalence and Strong Equivalence Between the Sparsest and Least l1-Norm Nonnegative Solutions of Linear Systems and Their Applications

Many practical problems can be formulated as l0-minimization problems with nonnegativity constraints,which seek the sparsest nonnegative solutions to underdetermined linear systems.Recent study indicates that l1-minimization is efficient for solving l0-minimization problems.From a mathematical point of view,however,the understanding of the relationship between l0-and l1-minimization remains incomplete.In this paper,we further address several theoretical questions associated with these two problems.We prove that the fundamental strict complementarity theorem of linear programming can yield a necessary and sufficient condition for a linear system to admit a unique least l1-norm nonnegative solution.This condition leads naturally to the so-called range space property(RSP)and the “full-column-rank”property,which altogether provide a new and broad understanding of the equivalence and the strong equivalence between l0-and l1-minimization.Motivated by these results,we introduce the concept of “RSP of order K”that turns out to be a full characterization of uniform recovery of all K-sparse nonnegative vectors.This concept also enables us to develop a nonuniform recovery theory for sparse nonnegative vectors via the so-called weak range space property.

1-Bit compressive sensing: Reformulation and RRSP-based sign recovery theory

Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit.