We discuss the phase diagram of Wilson fermions in the m0–g 2 plane for twoflavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki’s conjecture. We show that they are in fact consistent with the presence of a...

We compare the Hilbert series approach with explicit constructions of higher-order Lagrangians for $O(N)$ nonlinear sigma model. use to find number and type operators up mass dimension 16, spacetime $D$ 12 $N$ 12, further classify into parity internal symmetry group $O(N)$. The construction is done both parities even 10 other three cases. results two methods are in full agreement. This provides...

Here we perform a Kaluza–Klein dimensional reduction of Vasiliev’s first-order description massless spin-s particles from D=3+1 to D=2+1 and derive self-dual models describing with helicities ±s for the cases s=1,2,3. In first two recover known (parity singlets) models. spin-3 case new order model local Weyl symmetry which lifts traceless restriction on rank-3 tensor. A gauge fixed version this...

We show a new duality between the polynomial margin complexity of f and the discrepancy of the function f ◦XOR, called an XOR function. Using this duality, we develop polynomial based techniques for understanding the bounded error (BPP) and the weakly-unbounded error (PP) communication complexities of XOR functions. This enables us to show the following. • A weak form of an interesting conjectu...

We show a new duality between the polynomial margin complexity of f and the discrepancy of the function f ◦XOR, called an XOR function. Using this duality, we develop polynomial based techniques for understanding the bounded error (BPP) and the weakly-unbounded error (PP) communication complexities of XOR functions. This enables us to show the following. • A weak form of an interesting conjectu...

A graph G is strict quasi parity (SQP) if every induced subgraph of G that is not a clique contains a pair of vertices with no odd chordless path between them (an even pair). Hougardy conjectured that the minimal forbidden subgraphs for the class of SQP graphs are the odd chordless cycles, the complements of odd or even chordless cycles, and some line-graphs of bipartite graphs. Here we prove t...

eighteen primiparous rabbit does comprising of six per breed of new zealand white (nzw), chinchilla (cc) and dutch belted (db). they were randomly allocated to three rebreeding interval groups of 7, 14 and 21 days postpartum. three breeding males, one per breed were used giving a total of 21 rabbits. significant (p

Given an odd prime q and integer m ≤ q, a binary mq × q2 quasi-cyclic parity-check matrix H(m, q) can be constructed for array low-density (LDPC) code C(m, q). In this letter, we investigate the first separating redundancy of We prove that is 1-separating any pair (m, q), from which conclude upper bounded by mq. Then show our bound on tighter than general deterministic constructive bounds in li...

چکیده the issue of validity and non-validity of absolute conjecture, although frequently studied and researched by great scholars, is still in need of further research, since the studies and researches carried out so far are typically based on the presuppositions that have been regarded as indisputable and needless of study and research; whereas, in fact, they are not indisputable and need furt...

The problem of counting tilings by dominoes and other dimers and finding arithmetic significance in these numbers has received considerable attention. In contrast, little attention has been paid to the number of tilings by more complex shapes. In this paper, we consider tilings by trominoes and the parity of the number of tilings. We mostly consider reptilings and tilings of related shapes by t...