For a global field K and an elliptic curve Eη over K(T), Silverman's specialization theorem implies rank(Eη(K(T))) ≤ rank(Et(K)) for all but finitely many t ∈ P 1 (K). If this inequality is strict for all but finitely many t, the elliptic curve Eη is said to have elevated rank. All known examples of elevated rank for K = Q rest on the parity conjecture for elliptic curves over Q, and the exampl...

We study the parity of coefficients classical mock theta functions. Suppose g is a formal power series with integer coefficients, and let c(g;n) be coefficient qn in its expansion. say that type (a,1−a) if takes even values probability for n≥0. show among 44 functions, 21 them are (1,0). further conjecture 19 functions (12,12) 4 (34,14). also give characterizations n such odd

For a global field K and an elliptic curve Eη over K(T), Silverman's specialization theorem implies rank(Eη(K(T))) ≤ rank(Et(K)) for all but finitely many t ∈ P 1 (K). If this inequality is strict for all but finitely many t, the elliptic curve Eη is said to have elevated rank. All known examples of elevated rank for K = Q rest on the parity conjecture for elliptic curves over Q, and the exampl...

We study the query complexity of WEAK PARITY: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2+ε fraction of input strings, but must do so with high probability on those inputs where one does succeed. It is well-known that n randomized queries and n/2 quantum queries are needed to compute parity on all inputs. But surprisingly, we give a rando...

In this paper, some earlier results by Fleischner [H. Fleischner, Bipartizing matchings and Sabidussi’s compatibility conjecture, DiscreteMath. 244 (2002) 77–82] about edge-disjoint bipartizingmatchings of a cubic graphwith a dominating circuit are generalized for graphs without the assumption of the existence of a dominating circuit and 3-regularity. A pair of integer flows (D, f1) and (D, f2)...

conclusions increment in the number of parity can lead to decrease antioxidant defense mechanisms in multiparous women and their newborns. so, control of oxidative stress is considered to be beneficial in multiparous women. background parturition has been associated with free radicals, itself linked with poor pregnancy outcome. objectives this study aimed to investigate the relationship between...

Abstmct We reveal an equivalence relation between the construction of a new class of low density MDS array codes, that we call B-Code, and a combinatorial problem known as perfect one-factorization of complete graphs. We use known perfect one-factors of complete graphs to create constructions and decoding algorithms for both B-Code and its dual code. B-Code and its dual are optimal in the sense...

In this paper, we study the approximability of Max CSP(P ) where P is a Boolean predicate. We prove that assuming Khot’s d-to-1 Conjecture, if the set of accepting inputs of P strictly contains all inputs with even (or odd) parity, then it is NP-hard to approximate Max CSP(P ) better than the simple random assignment algorithm even on satisfiable instances. This is a generalization of a work by...

We show that an n-gap periodic quantum system with parity-even smooth potential admits 2n − 1 isospectral super-extensions. Each is described by a tri-supersymmetry that originates from a higher-order differential operator of the Lax pair and two-term nonsingular decompositions of it; its local part corresponds to a spontaneously partially broken centrally extended nonlinear N = 4 supersymmetry...

led Bender and Boettcher to conjecture that under suitable boundary conditions the spectrum of (1) was entirely real and positive provided M ≥ 1 [2]. Bender and Boettcher also noticed the relevance of PT -symmetry [2,3] to these problems. For all M , the potentials V (x) = −(ix)2M are invariant under the combined action of parity and time reversal, and this implies the eigenvalues are either re...