Inspired by the recent observation of $\chi_{c0}(3930)$, $X(4685)$ and $X(4630)$ LHCb Collaboration some exotic resonances such as $X(4350)$, $X(4500)$, etc. several experiment collaborations, $cs\bar{c}\bar{s}$ tetraquark systems with $IJ^{P}=00^+$, $01^+$ $02^+$ are systematically investigated in framework quark delocalization color screening model(QDCSM). Two structures, meson-meson diquark-...

We show that for U (1)-symmetric spacetimes on S 3 × R a constant of motion associated with the well known Geroch transformation, a functional K[h ij , π ij ], quadratic in gravitational momenta, is strictly positive in an open subset of the set of all U (1)-symmetric initial data, and therefore not weakly zero. The Mixmaster initial data appear to be on the boundary of that set. We calculate t...

Let A = (a ij) be a real n n matrix with non-negative entries which are weakly increasing down columns. If B = (b ij) is the nn matrix where b ij := a ij +z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.

(A) Let Q(A) be number of comparisons done on input array A: (A) R ij : event that rank i element is compared with rank j element, for 1 ≤ i < j ≤ n. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. (B) Q(A) = ∑ 1≤i<j≤n X ij. (C) By linearity of expectation,