Summation formulae for q-series with independent bases are obtained and used to derive transformation and expansion of q-series involving independent bases.

This paper is devoted to the study of independent spaces q-polymatroids. With aid an auxiliary q-matroid it shown that collection satisfies same properties as for q-matroids. However, in contrast q-matroids, rank value space does not agree with its dimension. Nonetheless, values fully determine q-polymatroid, and this fact can be exploited derive a cryptomorphism Finally, notions minimal spanni...

In this note, we show that if N = q^kn^2 is an odd perfect number with special prime q, and not divisible by 3, then the inequality q < n holds. We give another unconditional proof for which independent of results Brown Starni.

Let $\Gamma$ be the graph whose vertices are chambers of finite projective space $\mathrm{PG}(3,q)$ with two being adjacent when corresponding in general position. It is known that independence number this $(q^2+q+1)(q+1)^2$. For $q\geqslant 43$ we determine largest independent set and show every maximal not a one has at most constant times $q^3$ elements. 47$, information then used to chromati...

We study the energy and entropies for $N$ independent harmonic oscillators in microcanonical canonical ensembles Tsallis classical quantum statistics of entropic parameter $q$, where is number value $q$ larger than one. The are represented with physical temperature, well-known expressions obtained R\'enyi entropy. difference between existence condition ensemble: $N(q-1)<1$. does not appear ense...

Motivated by the work of Zargar and Zamani, we introduce a family elliptic curves containing several one- (respectively two-) parameter subfamilies high rank over function field $\mathbb{Q}(t)$ $\mathbb{Q}(t,k)$). Following approach Moody, construct two infinitely many at least 5 $\mathbb{Q}(t,k)$. Secondly, deduce other this family, induced edges rational cuboid five independent $\mathbb{Q}(t)...

background: prevention of slipping accidents requires provision of adequate friction through the use of suitable combinations of footwear and underfoot surfaces. shoe sole tread groove is one of the important factors on friction coefficient during walking. objective: to measure the effect of different shoe sole tread groove depths and different surfaces on the required quotient of friction (q),...

We consider pairs of automorphisms $(\phi,\sigma)$ acting on fields Laurent or Puiseux series: shift operators $(\phi\colon x\mapsto x+h\_1, \sigma\colon x+h\_2)$, $q$-difference q\_1x$, $\sigma\colon q\_2x)$, and Mahler x^{p\_1},\ x^{p\_2})$. Given a solution $f$ to linear $\phi$-equation $g$ an algebraic $\sigma$-equation, both transcendental, we show that are algebraically independent over t...

The chiral effective meson-baryon Lagrangian for the description of interactions between doubly charmed baryons and Goldstone bosons is constructed up to order $q^{4}$. numbers linearly independent invariant monomials $\mathcal{O}(q^2)$, $\mathcal{O}(q^3)$ $\mathcal{O}(q^4)$ are 8, 32 218, in order. obtained can be used study dynamics relevant phenomenology at complete one-loop level future. Fo...

In this letter, we discuss certain universal predictions of the large charge expansion in conformal field theories with $U(1)$ symmetry, mainly focusing on four-dimensional theories. We show that, while three dimensions quantum fluctuations are responsible for existence a theory-independent $Q^0$ term scaling dimension $\Delta_Q$ lightest operator fixed $Q\gg 1$, four same mechanism provides $Q...