Convex Structure Research Articles

Analysis of the skin surface and inner structure around pores on the face

Facial pores do not appear to close again in old skin. Therefore, the tissue structure around the pore has been speculated to keep the pore open. To elucidate the reason for pore enlargement, we examined the relationship between the skin surface and inner skin structural characteristics in the same regions especially around the pore. Samples of the skin surface were obtained from the cheek and examined using a laser image processor to obtain three-dimensional (3D) data. The inner structure of the skin was analyzed using in vivo confocal laser scanning microscopy (CLSM). The conspicuous pore not only had a concave structure but also a discontinuous convex structure on the skin surface surrounding the pore. Furthermore, CLSM image indicated that the skin inner structure developed a discontinuous dermal papilla structure and isotropic dermal fiber structure. There were structural changes in the skin surface around conspicuous pores, including not only a concave structure but also a convex structure with skin inner structure changing.

Robust estimation of location and scatter by pruning the minimum spanning tree

One of the most essential topics in robust statistics is the robust estimation of location and covariance. Many popular robust (location and scatter) estimators such as Fast-MCD, MVE, and MZE require at least a convex distribution of the underlying data. In the case of non-convex data distributions these approaches may lead to a suboptimal result caused by the application of Mahalanobis distances with respect to location and covariance of a suitably chosen subsample of the data—implying a convex structure. The approach presented here fixes this drawback using Euclidean distances. The data set is treated as a complete network and the minimum spanning tree (MST) for this data set is calculated. Based on the MST a subset of relevant points (thought of as an “outlier-free” subsample of minimum size) is determined which can then be used for calculating data characteristics. It is shown, that the approach has a maximum breakdown point. Additionally, a simulation study provides insights in the approach’s behaviour with respect to increasing dimension and size.

Numerical investigation of the effect of cathode holder shape on hafnium cathode evaporation for an oxygen plasma cutting arc

The effects of cathode holder shape on a plasma cutting arc were investigated using a two-dimensional thermo-fluid model developed for arc plasmas with the consideration of hafnium cathode evaporation. The shape of the cathode holder was defined by a convex structure, which protruded from the surface of the cathode holder. Results showed that the vortex of gas flow near the hafnium cathode was created by the effect of the convex cathode holder. The temperature of the cathode surface decreased markedly with higher protrusion of the convex cathode holder by a rapid clockwise rotation of the gas flow. The presence of gas flow vortex towards the cathode surface reduced the mass fraction of hafnium vapour near the surface cathode. Finally, the total amount of mass loss of hafnium evaporation was predicted to decrease markedly with the effect of the convex cathode holder.

Several new inequalities on operator means of non-negative maps and Khatri–Rao products of positive definite matrices

In this paper, we provide some interested operator inequalities related with non-negative linear maps by means of concavity and convexity structure, and also establish some new attractive inequalities for the Khatri–Rao products of two or more positive definite matrices. These results lead to inequalities for Hadamard product and Ando’s and α-power geometric means, as a special case.

Relay Beamforming Designs in Multi-User Wireless Relay Networks Based on Throughput Maximin Optimization

Beamforming design for multi-user wireless relay networks under the criterion of maximin information throughput is an important but also very hard optimization problem due to its nonconvex nature. The existing approach to reformulate the design as a matrix rank-one constrained optimization problem is highly inefficient. This paper exploits the d.c. (difference of two convex functions) structure of the objective function and the convex structure of the constraints in such a global optimization problem to develop efficient iterative algorithms of very low complexity to find the solutions. Both cases of concurrent and orthogonal transmissions from sources to relays are considered. Numerical results indicate that the proposed algorithms provide solutions that are very close to the upper bound on the solution of the non-orthogonal source transmissions case and are almost equal to the optimal solution of the orthogonal source transmissions case. This demonstrates the ability of the developed algorithms to locate approximations close to the global optimal solutions in a few iterations. Moreover, the proposed methods are superior to other methods in both performance and computation complexity.

Quantum dynamics study on the exchange H + OH+ reaction

The time-dependent wave packet quantum method under centrifugal sudden (CS) approximation has been employed to investigate the dynamics of the exchange reaction H+OH+ based on an accurate potential energy surface [Martínez et al., J. Chem. Phys. 120 (2004) 4705]. The reaction probability dependence with collision energy, the weighed partial wave contributions to the integral cross sections, and the integral cross sections of the exchange reaction H+OH+ in the collision energy range of 0.0–1.0eV with reactant OH+ in the rotational state ji=0 and vibrational states vi=0–4 are calculated. The calculated time evolution of CS probability density distribution in logarithmic scales at total angular momentum J=0 clearly indicates that the convex structure in the reaction path of the exchange H+OH+ reaction has significant influence on the dynamics of title reaction.

Quantum Dynamics Study on D+OD+ Reaction: Competition between Exchange and Abstraction Channels

Quantum dynamics for the D+OD+ reaction at the collision energy range of 0.0–1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction (D+OD+→O++D2) and thermoneutral exchange (D+OD+→D+OD+) channels were investigated from the same set of time-dependent quantum wave packets method under centrifugal sudden approximation. The reaction probability dependence with collision energy, the integral cross sections, and the thermal rate constant of the both channels are calculated. It is found that there is a convex structure in the reaction path of the exchange reaction. The calculated time evolution of the wave packet distribution at J=0 clearly indicates that the convex structure significantly influences the dynamics of the exchange and abstraction channels of title reaction.

A polynomial approach for optimal control of switched nonlinear systems

Optimal control problems for switched nonlinear systems are investigated. We propose an alternative approach for solving the optimal control problem for a nonlinear switched system based on the theory of moments. The essence of this method is the transformation of a nonlinear, nonconvex optimal control problem, that is, the switched system, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high-performance numerical computing. Consequently, we propose to convexify the control variables by means of the method of moments obtaining semidefinite programs. Copyright © 2013 John Wiley & Sons, Ltd.

Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure

Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure

A New Fixed Point Theorem and Applications

A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space) without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.

Estrutura subsuperficial do Complexo Alcalino do Mendanha, Rio de Janeiro, por integração de dados geológicos e gravimétricos

Esse trabalho apresenta os resultados de pesquisas geológicas e gravimétricas realizadas na região do Complexo Alcalino do Mendanha. As técnicas aplicadas foram de mapeamento geológico básico 1:50.000 e gravimetria terrestre, com equipamentos LaCoste & Romberg, com controle de posicionamento por GPS diferencial. A análise integrada dos dados permitiu gerar seções e modelos gravimétricos 2,5D, estimando a geometria da suíte alcalina em subsuperfície. O Complexo Alcalino do Mendanha é constituído por rochas de composição sienítica de granulometria variável, com predominância de álcali-sienitos, sienitos e rochas piroclásticas na região do "Vulcão de Nova Iguaçu" e de sienitos com nefelina, na região do Morro do Marapicu. Rochas sieníticas possuem densidade média de 2,54g/cm³ e rochas piroclásticas, 2,46g/cm³, medidas em laboratório. Em comparação com gnaisses encaixantes (2,68g/cm³), produzem anomalias gravimétricas negativas. O modelo gravimétrico da região do "Vulcão de Nova Iguaçu" ilustra uma geometria em forma de funil, formada por rochas sieníticas e uma estrutura colunar (conduto) de rochas piroclásticas. O modelo para o Morro do Marapicu apresenta uma estrutura convexa rasa, que é interpretada como continuidade do Mendanha. Com isso, o estágio de denudação atual caracteriza porção basal de câmara magmática, com exibição de conduto piroclástico e diques alimentadores.

Support Effect and Application of High Convex Steel-Belt in Deep Roadway

The steel-belt has the ability to improve support effect of the whole system that coordinate the anchorage force of bolt or cable, improve the support effect of the anchor system and diffuse the fore acted on bolt or cable. During the progress of support in the roadway, there has appeared flat, W and M steel-belt, and all of them have played important roles in different stages of support in the roadway. However, steel-belt now is rarely used in the deep rock roadway. High convex steel-belt is a new product, but whether it can adapt or not to the deep roadway, it's well worth our attention. The structure of high convex steel-belt and the characteristics of deep roadway are introduced in this paper. Numerical test on four kinds of mine steel-belt is carried out by ANSYS, and the advantage of high convex steel-belt is comparatively analyzed in deep roadway. At last, an example is shown. Research indicates that the steel-belt bears mainly the point load or local load due to non smooth and even convex wall sides, and it lies in a state of inelastic and large deformation due to non uniformity deformation of surrounding rock in the deep rock roadway. The mechanical behavior of convex steel-belt has the performance of obvious advantages. It can adapt to the large deformation of deep roadway due to the convex structure. This result has been proved in the engineering practice.

Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our approach is applicable to general entanglement measures and states and is an efficient alternative to the conventional approach based on the optimal pure-state decomposition. Compared with the conventional one, it has two important merits: (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the W state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator and of the convex structure of mixed states, which are related to the symmetry and the rank of states.

Ground-state spaces of frustration-free Hamiltonians

We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of “reduced spaces” to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set Θk of all the k-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in Θk, called atoms, are analogs of extreme points. We study the properties of atoms in Θk and discuss its relationship with ground states of k-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in Θ2 are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in Θk may not be the join of atoms, indicating a richer structure for Θk beyond the convex structure. Our study of Θk deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from the new perspective of reduced spaces.

Reactive Solid Surface Morphology Variation via Ionic Diffusion

In gas-solid reactions, one of the most important factors that determine the overall reaction rate is the solid morphology, which can be characterized by a combination of smooth, convex and concave structures. Generally, the solid surface structure varies in the course of reactions, which is classically noted as being attributed to one or more of the following three mechanisms: mechanical interaction, molar volume change, and sintering. Here we show that if a gas-solid reaction involves the outward ionic diffusion of a solid-phase reactant then this outward ionic diffusion could eventually smooth the surface with an initial concave and/or convex structure. Specifically, the concave surface is filled via a larger outward diffusing surface pointing to the concave valley, whereas the height of the convex surface decreases via a lower outward diffusion flux in the vertical direction. A quantitative 2-D continuum diffusion model is established to analyze these two morphological variation processes, which shows consistent results with the experiments. This surface morphology variation by solid-phase ionic diffusion serves to provide a fourth mechanism that supplements the traditionally acknowledged solid morphology variation or, in general, porosity variation mechanisms in gas-solid reactions.

One-local retract and common fixed point in modular function spaces

In this paper, we introduce and study the concept of one-local retract in modular function spaces. In particular, we prove that any commutative family of ρ-nonexpansive mappings defined on a nonempty, ρ-closed and ρ-bounded subset of a modular function space has a common fixed point provided its convexity structure of admissible subsets is compact and normal.

Comment on some results of Erdahl and the convex structure of reduced density matrices

In [J. Math. Phys. 13, 1608–1621 (1972)], Erdahl10.1063/1.1665885 considered the convex structure of the set of N-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the m-body setting and to the more general quantum marginal problem. We describe these extensions, but cannot resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when 2m ⩾ N every extreme point of the set of N-representable m-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary m-body and (N − m)-body reduced density matrices.

Analysis of the responses of termites to tunnel irregularity

Subterranean termites build extensive underground galleries consisting of elaborate tunnels and channels to forage food resources. Diverse soil conditions surrounding the tunnels, such as soil density, may cause irregularities in the size and shape of the tunnels, and termites are likely to encounter a number of tunnel irregularities while traveling. Considering the tunnel length, how termites respond to an irregularity is likely to affect their movement efficiency, and this in turn is directly correlated to their foraging efficiency. To understand the response of termites, we designed an artificial linear tunnel with rectangular irregularities in a 2-D arena. The tunnel widths, W, were 3 and 4 mm. The rectangular irregularities were 2 mm in width and of varying heights H (2, 1, 0, −1, and −2 mm). The positive and negative sign of H represents a convex and concave structure, respectively. We systematically observed the movement of termites, Coptotermes formosanus Shiraki, at the irregularity and quantified the time needed, τ, for a termite to pass the irregularity. The time τ was shorter for (W, H) = (3, 0) and (3, −1) than for (W, H) = (3, 1), (3, 2), and (3, −2). The time τ was longer for (W, H) = (4, −1), and (4, −2), than for (W, H) = (4, 0), (4, 1) and (4, 2). Four types of behaviors explained the response to the irregularity. The implications of these findings are briefly discussed in relation to termite foraging efficiency.

Analysis on formation mechanism of ultra-smooth surfaces in atmospheric pressure plasma polishing

Atmospheric pressure plasma polishing (APPP) is developed for the final finishing of high quality ultra-smooth surfaces. To improve surface quality, formation mechanism of ultra-smooth surfaces in APPP is studied. Quantum chemistry simulation is used to investigate the interaction between atoms. Simulation of single Si-F bonding process indicates 0.2 eV difference of binding energy between convex and concave models, which reflects the reaction probability of convex structure is higher than that of concave structure. By comparing the spatial atomic configuration and species diffusion path, it is also demonstrated convex topography should be removed faster than concave topography. So roughness of optical surfaces can be reduced further to form ultrasmooth surfaces. And experimental results accord well with theoretical analysis. Detected by atomic force microscopy every 40 s, the average maximum height of surface is testified to decrease faster than the maximum depth obviously, which makes the whole surface going toward a new equilibrium status with lower roughness. Another experiment proves the average surface roughness decreases from Ra 4.529 to 0.926 nm after 100 s continuous machining. And the stereo images also indicate obvious improvement of surface topography. Moreover, free outmost electron is proved to be helpful to promote chemical reaction by simulation, so fresh surfaces may be more favorable for APPP which makes sample preparation more purposeful.

Transversal numbers over subsets of linear spaces

Let M be a subset of R-k. It is an important question in the theory of linear inequalities to estimate the minimal number h = h(M) such that every system of linear inequalities which is infeasible over M has a subsystem of at most h inequalities which is already infeasible over M. This number h(M) is said to be the Helly number of M. In view of Helly's theorem, h(R-n) = n+1 and, by the theorem due to Doignon, Bell and Scarf, h(Z(d)) = 2(d). We give a common extension of these equalities showing that h(R-n x Z(d)) = (n + 1)2(d). We show that the fractional Helly number of the space M subset of R-d (with the convexity structure induced by R-d) is at most d+1 provided h(M) is finite. Finally we give estimates for the Radon number of mixed integer spaces.