Abstract The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called q -bracket, is quasimodular form. More generally, if graded A -bracket every element form same weight, we call algebra. We introduce new $$\mathcal {T}$$ T con...

In this paper we study plane conic geometry, particularly different representations of geometric constructions and relations in plane conic geometry, with Cayley and bracket algebras. We propose three powerful simplification techniques for bracket computation involving conic points, and an algorithm for rational Cayley factorization in conic geometry. The factorization algorithm is not a genera...

Abstract. Following Rankin’s method, D. Zagier computed the n-th Rankin-Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2 and then computed the inner product of this Rankin-Cohen bracket with a cusp form f of weight k = k1 + k2 + 2n and showed that this inner product gives, upto a constant, the special value of the Rankin-Selberg convolution of f and g. This...

We investigate differential operators and their compatibility with subgroups of SL2(R) n. In particular, we construct Rankin–Cohen brackets for Hilbert modular forms, and more generally, multilinear differential operators on the space of Hilbert modular forms. As an application, we explicitly determine the Rankin– Cohen bracket of a Hilbert–Eisenstein series and an arbitrary Hilbert modular for...

We present a natural multiplicative theory of integer partitions (which are usually considered in terms of addition), and find many theorems of classical number theory arise as particular cases of extremely general combinatorial structure laws. We then see that the relatively recently-defined q-bracket operator 〈f〉q, studied by Bloch– Okounkov, Zagier, and others for its quasimodular properties...

The superconformal algebras of Ademollo et al are generalised to a multi-index form. The structure obtained is similar to the Moyal Bracket analogue of the Neveu-Schwarz Algebra.

The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and JPY /DEM and DEM/USD currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and random influences on these financial time series we perform a statistical analysis of their increments ∆x(...

The purpose of the study was to measure and compare the level of frictional resistance generated between conventional ceramic brackets (Transcend Series 6000, 3M Unitek, Monrovia, Calif), ceramic brackets with stainless steel slot (Clarity, 3M Unitek), conventional stainless steel brackets (Victory Series, 3M Unitek), and 3 different orthodontic wire alloys: stainless steel (stainless steel, SD...

Little is known about the performance of Transbond Plus Self-Etching Primer (TPSEP), especially when used with Adhesive Precoated Brackets (APC 1 and APC 2). The aim of this study was to compare the shear bond and rebond strengths and failure sites of APC 1 and APC 2 with a non-coated bracket system [Victory Series (V)] using Transbond XT light-cured adhesive and TPSEP or 37 percent phosphoric ...

background and aims. the aim of this study was to compare shear bond strength (sbs) of metal and ceramic brackets bonded to enamel using acid versus er:yag laser etching. materials and methods. eighty premolars were divided into 4 groups: am (acid etching/ metal brackets), ac (acid etching/ ceramic brackets), lm (laser etching/ metal brackets) and lc (laser etching/ ceramic brackets). enamel co...