In this paper we give two results about analytic sets. The rst is a counterexample to a problem of Fremlin. We show that there exists ! 1 compact subsets of a Borel set with the property that no -compact subset of the Borel set covers them. In the second section we prove that for any analytic subset A of the plane either A can be covered by countably many lines or A contains a perfect subset P ...

The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

Ca influx via Ca current (ICa) during the action potential (AP) was determined at 25°C and 35°C in isolated rabbit ventricular myocytes using AP clamp. Contaminating currents through Na and K channels were eliminated by using Naand K-free solutions, respectively. DIDS (0.2 mmol/L) was used to block Ca-activated chloride current (ICl(Ca)). When the sarcoplasmic reticulum (SR) was depleted of Ca ...

For simplicity, we use the following convention: i, i1, i2, j, j1, j2, k, m, n, t denote natural numbers, D denotes a non empty subset of E2 T, E denotes a compact non vertical non horizontal subset of E2 T, C denotes a compact connected non vertical non horizontal subset of E2 T, G denotes a Go-board, p, q, x denote points of E2 T, and r, s denote real numbers. The following propositions are t...

Membrane depolarization inactivates acetylcholine receptor (AChR) genes in skeletal muscle. We have studied this process in C2C12 cells, focusing on the role of calcium. Cytoplasmic calcium was monitored with fluo-3, and the activity of receptor genes was measured with a sensitive transcript elongation assay. Removal of extracellular calcium or blockage of L-type calcium channels disrupts signa...

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...

Let L be a positive line bundle over a projective complex manifold X , L its tensor power of order p, H(X,L) the space of holomorphic sections of L and Np the complex dimension of H(X,L). The determinant of a basis ofH(X,L), together with some given probability measure on a weighted compact set in X , induces naturally a βensemble, i.e., a random Np-point process on the compact set. Physically,...

The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of R which is Baire (= has the property, BP) or measurable shift-compact: it contains some subsequence any null sequence to within translation by an element set. Here effective proofs are recognized yield (i) analogous category and Haar-measure metrizable generalizations for groups locally compact respectively, (ii) permit...

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.