Algebraic structures in which the property of commutativity is substituted by mediality are introduced. We consider (associative) graded algebras and instead almost (generalized or $\varepsilon$-commutativity) we introduce ("commutativity-to-mediality" ansatz). Higher twisted products "deforming" brackets (being medial analog Lie brackets) defined. Toyoda's theorem connects (universal) with abe...

When a real-valued function of one variable is approximated by its n th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f (n) or f (n+1) are Henstock–Kurzweil integrable. When the only assumption is that f (n) is Henstock–Kurzweil integrable then a modified form of the n th degree Taylor polynomial is used. When the only assumption i...

We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 ≤ j ≤ n) of a connected graph Γ on n vertices, then μj ≥ dj − j + 2 (1 ≤ j ≤ n− 1). This settles a conjecture due to Guo.

We present a technique for automatically generatingcommutativity conditions from (abstract-level) data-structurespecifications. We observe that one can pose the commutativityquestion in a way that does not introduce additional quantifiers,via a mechanized lifting of a (potentially partial) specificationto an equivalent total specification. We then describe an al-gorithm ...

In this paper are determined minimal shape-preserving projections onto the n-th degree algebraic polynomials.

There are many methods to solve equation of degree n with one unknown, but the restrictions most very harsh. Based on Vieta’s theorem, this paper gives symbolic effective coefficient method and elimination rotation symmetry n-th variable.

We perform a perturbative O(g4) Wilson loop calculation for the U(N) YangMills theory defined on non-commutative one space one time dimensions. We choose the light-cone gauge and compare the results obtained when using the Wu-Mandelstam-Leibbrandt (WML) and the Cauchy principal value (PV ) prescription for the vector propagator. In the WML case the θ-dependent term is well-defined and regular i...

In this paper, based on recent work [13] 1 , we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this new interpretation of superPoincaré algrebra as our fundamental symmetry, we can construct Lorentz and Poincaré SUSY invariant quantum field theory on the non(anti)commutative (super)space. The key point is validity of our new twist element that guarantee...