We consider the class of integer rectifiable currents without boundary in Rn × R satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this note, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and various examples are given. Given y ∈ R and a b...

We introduce a new class of control problems in which the gain depends on the solution of a stochastic differential equation reflected at the boundary of a bounded domain, along directions which are controlled by a bounded variation process. We provide a PDE characterization of the associated value function. This study is motivated by applications in mathematical finance where such equations ar...

We analyze the variation of prices in a model of an exchange market introduced by Kakade et al. [11], in which buyers and sellers are represented by vertices of a bipartite graph and trade is allowed only between neighbors. In this model the graph is generated probabilistically, and each buyer is connected via preferential attachment to v sellers. We show that even though the tail of the degree...

We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis. 5

Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation (Lipschitzian or monotonic) are given. Applications in relation with the well-known Čebyšev, Grüss, Ostrowski and Lupaş inequalities are provided as well.

We prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of Lie type of bounded rank is bounded. For exceptional groups this solves a longstanding open problem. The proof uses, among other tools, some methods from Geometric Invariant Theory. Using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of L...

The classical Sobolev embedding theorem of the space of functions of bounded variation BV (Rn) into Ln (Rn) is proved in a sharp quantitative form.

Let X = (X; . . . ; X) be a continuous semimartingale and let b : IR 1 ! IR be a continuous function such that the process b = b(X; . . . ; X ) is a semimartingale. Setting C = f (x1; . . . ; xn) 2 IR j xn < b(x1; . . . ; xn 1) g and D = f (x1; . . . ; xn) 2 IR j xn > b(x1; . . . ; xn 1) g suppose that a continuous function F : IR ! IR is given such that F is C1n on C and F is C1 ;...;in on D w...

An interfacing circuit for piezoresistive pressure sensors based on CMOS current conveyors is presented. The main advantages of the proposed interfacing circuit include the use of a single piezoresistor, the capability of offset compensation, and a versatile current-mode configuration, with current output and current or voltage input. Experimental tests confirm linear relation of output voltage...