A Markoff-type chain for the view-obstruction problem for spheres in ℝ4

In the view-obstruction problem, congruent, closed, convex bodies centred at the points in ⁿ are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1, this value is denoted byv(n) and is known for dimensionsn=2,3. Here we show that and obtain a Markoff type chain of isolated extreme values.     

Regularity results for p-harmonic functions in higher order Grušin planes

We study the interior regularity for nondegenerate p-harmonic functions in Grušin planes of higher order. The local boundedness of the horizontal gradient is obtained by running a subelliptic variant of the Moser iteration scheme.     

The view-obstruction problem for spheres in ℝ5

In the view-obstruction problem, congruent, closed convex bodies centred at the points in ⁿ are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1 and cubes of side 1 these values are known forn=2, 3 and 4. Here we show that in ⁵, this value for the sphere of diameter 1 is .     

Group LASSO for Change-points in Functional Time Series

Multiple change-points estimation for functional time series is studied in this paper. The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions. Group least absolute shrinkage and selection operator(LASSO) is then applied to estimate the number and the locations of possible change points. However, the group LASSO(GLASSO)always overestimate the true points. To circumvent this problem, a further Information Criterion(IC) is applied to elim...     

A Pinching Theorem for Minimal Submanifolds in Sphere

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Convolution operators in A ?∞ for convex domains

We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂ ⁿ and have a polynomial growth near its boundary. A characterization of the surjectivity of such operators on the class of all domains is given in terms of low bounds of the Laplace transformation of analytic functionals defining the operators.     

Double Bubbles for Immiscible Fluids in ℝ n

We use a new approach that we call unification to prove that standard weighted double bubbles in n-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for weighted area, and also gives the simplest known proof to date of the (unit weight) double bubble theorem (Hass et al., Electron. Res. Announc. Am. Math. Soc., 1(3):98–102, 1995; Hutchings et al., Ann. Math., 155(2):459–489, 2002; Reichardt, J. Geom. Anal., 18(1):172–191, 2008). As part of the proof, we introduce a striking new symmetry argument for showing that a minimizer must be a surface of revolution.     

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R~N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.     

E-learning in secondary–tertiary transition in mathematics: for what purpose?

Mathematics is a challenging subject for many science freshmen, and failing mathematics exams is a major factor in university dropout rates. Many factors, including metacognitive, affective and linguistic ones, play a role in students?? difficulties in mathematics. Starting from this perspective, we conducted a theoretical exploration of the potential of online environments in helping students counteract the mathematical difficulties they face in the transition from secondary school to university. Although this secondary?Ctertiary transition and the use of technology are both widely researched issues in mathematics education, the potential of technology in helping students in the ??rite of passage?? to tertiary education has not yet been researched. This paper reports on the developed theoretical framework and on the preliminary findings from the implementation of an e-learning course that we designed with the aim of supporting students in the critical phase of transition from secondary school to university.     

Emergy analysis for ‘Four in One’ peach production system in Beijing

‘Four in One’ production system has been widely used for recent years in rural areas of Beijing. The aim of this study is to assess the efficiency and sustainability of the ‘Four in One’ ecological economic system for peach production system (FIOPPS) in the solar greenhouse in Pinggu district, Beijing, by emergy-based ecological analysis. The emergy-based indicators of the FIOPPS are calculated and compared with those of the conventional solar greenhouse peach production system. By comparison, the FIOPPS is proved to be more sustainable with less pressure on the environment, better economic benefit and higher efficiency of agricultural resource utilization, thus worthy of being generalized to boost the ecological agriculture in the rural areas of China.     

The Star-Kernel for a Quasidifferentiable Function in One-Dimensional Space

Let f be a function from R~1 into R~1. Suppose f is quasidifferentiable at x∈R~1. The following results have been obtained. Lemma We denote be A:=〔a_1,a_2〕and B:=〔b_1,b_2〕two intervals.Then〔A,B〕∈f(x) if and only if a_2+b_1=f′(x;+1), a_1+b_2=-f′(x;-1)hold, where f(x) denotes the quasidifferential set of f at x ∈R~1. Theorem 2 There exists a quasidifferential 〔f(x),f(x)〕∈f(x) suchthat     

Limiting theorems for the nodes in binary search trees

We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X_n, Y_n and Z_n are all asymptotically normal as n→∞by applying the contraction method.     

Extracting factors for students’ motivation in studying mathematics

The purpose of this article is to identify factors that statistically explain the variation and the measures on the level of motivation of a sample of mathematics students in a university. Specifically, this analysis will identify groups of similar items and reduce the number of variables used in a study. This article explains the use of exploratory factor analysis in extracting factors of personal belief and motivational factors among students in learning mathematics. The adaptation of these factors can be used for assessing academic performance in relation to motivation level. By identifying these factors, the mathematics educators or researchers will be able to find ways to improve the condition of the factors and also to further investigate the factors based on confirmatory approaches.     

Set of ambiguous points for functions in ℝ n

It is known that an arbitrary function in the open unit disk can have at most countable set of ambiguous points. Point ζ on the unit circle is an ambiguous point of a function if there exist two Jordan arcs, lying in the unit ball, except the endpoint ζ, such that cluster sets of function along these arcs are disjoint. We investigate whether it is possible to modify the notion of ambiguous point to keep the analogous result true for functions defined in the n-dimensional Euclidean unit ball.     

Hardy spaces for α-harmonic functions in regular domains

We investigate Hardy spaces H ^p for singular α-harmonic functions in bounded domains with regular boundaries. We show the correspondence between these spaces and suitable L ^p spaces and measure spaces.     

Invariants and Bonnet-type theorem for surfaces in ℝ4

In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes of surfaces in the four-dimensional Euclidean space, determined by conditions on their invariants, can be interpreted in terms of the properties of two geometric figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We construct a family of surfaces with flat normal connection.     

Testing for the maximum cell probabilities in multinomial distributions

This paper investigates one-sided hypotheses testing for p, the largest cell probability of multinomial distribution. A small sample test of Ethier (1982) is extended to the general cases. Based on an estimator of p, a kind of large sample tests is proposed. The asymptotic power of the above tests under local alternatives is derived. An example is presented at the end of this paper.     

Functional Limit Theorems for d-dimensional FBM in HSlder Norm

In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.