In recent years, the idea of sub- and super-Chandrasekhar limiting mass white dwarfs (WDs), which are potential candidates to produce under- over-luminous type Ia supernovae, respectively, has been a key interest in scientific community. Although researchers have proposed different models explain these peculiar objects, modified theories Einstein's gravity, particularly f(R) gravity with R bein...

A predicate f : {−1, 1} 7→ {0, 1} with ρ(f) = Ex∈{−1,1}k [f(x)] is said to be strongly approximation resistant if, for every ε > 0, given a near-satisfiable instance of MAX k-CSP(f), it is hard to find an assignment such that the fraction of constraints satisfied is outside the range [ρ(f)−ε, ρ(f) +ε]. A predicate which is not strongly approximation resistant is known as weakly approximable. We...

We find the universal module w(M) for functions (that need not be invariants) of finite matroids, defined on a minor-closed class M and with values in any module L over any commutative and unitary ring, that satisfy a parametrized deletion-contraction identity, F (M) = δeF (M r e) + γeF (M/e), when e is neither a loop nor a coloop. (F is called a (parametrized) weak Tutte function.) Within the ...

In this paper, we introduce a new class of local consistencies, called f -consistencies, for qualitative constraint networks. Each consistency of this class is based on weak composition ( ) and a mapping f that provides a covering for each relation. We study the connections existing between some properties of mappings f and the relative inference strength of f -consistencies. The consistency ob...

In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy wdF (P ) of a poset P = (V,≺) to be the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a) − f...

In this paper, we introduce a new class of local consistencies, called f -consistencies, for qualitative constraint networks. Each consistency of this class is based on weak composition ( ) and a mapping f that provides a covering for each relation. We study the connections existing between some properties of mappings f and the relative inference strength of f -consistencies. The consistency ob...

It is known that for Ω a connected separable metric space, a function Ω → R which at every point attains a weak local extremummust have countable image. Let Ω ⊂ R be a bounded domain and f : Ω → C a measurable, bounded, quasi-continuous function. For n ∈ Z+, we show that if |f | has countable image then f attains weak local extremum at each point of a dense open subset. We show by examples the ...

Let (Ω,Σ, μ) be a measure space and let 1 < p < ∞. The weak L space L(Ω,Σ, μ) consists of all measurable functions f such that ‖f‖ = sup t>0 t 1 p f∗(t) < ∞, where f∗ is the decreasing rearrangement of |f |. It is a Banach space under a norm which is equivalent to the expression above. In this paper, we pursue the problem of classifying weak L spaces isomorphically when (Ω,Σ, μ) is purely atomi...

Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) → P(N0) such that the induced function f : E(G)→ P(N0) is defined by f(uv) = f(u)+f(v), where f(u)+f(v) is the sumset of f(u) and f(v). An IASL f is said to be an integer additive set-indexer (IASI) if the associated edge-function...

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...