With the help of computer symbolic computation software e.g., Maple , abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equati...

In this paper we investigate under what conditions is a mapping f of a semigroup S into the class of cardinals representable by a groupoid G and a homomorphism g of G onto S such that ker(g) is the associativity congruence of G and Card(g(x)) = f(x) for every x ∈ S. Abstrakt. V tomto článku vyšetřujeme, za jakých podmı́nek lze zobrazeńı f pologrupy S do tř́ıdy všech kardinálńıch č́ısel reprezentov...

In the paper, the authors prove that the generalized sine function sinp,q(x) and the generalized hyperbolic sine function sinhp,q(x) are geometrically concave and geometrically convex, respectively. Consequently, the authors verify a conjecture posed in the paper “B. A. Bhayo and M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory 164 (2012), no. 10, 1415–...

We study relations of the Weierstrass’s hyperelliptic al-functions over a non-degenerated hyperelliptic curve y = f(x) of arbitrary genus g as solutions of sine-Gordon equation using Weierstrass’s local parameters, which are characterized by two ramified points. Though the hyperelliptic solutions of the sine-Gordon equation had already obtained, our derivations of them is simple; they need only...

We study the general problem of behaviour continuum function in presence non-supercompact strongly compact cardinals. begin by showing that it is possible to force violations GCH at an arbitrary cardinal using only strong compactness as our initial assumption. This result due third author. then investigate realising Easton functions and above least measurable limit supercompact cardinals starti...

In this paper, we provide a concise proof of Oppenheim’s double inequality relating to the cosine and sine functions. In passing, we survey this topic.

In this note, using the multisection series method, we establish the formulas for various power sums of sine or cosine functions.

A cardinal related to compositions of Sierpiński–Zygmund functions from the left, cleft(SZ), will be considered. We answer a question of K. Ciesielski and T. Natkaniec. In particular, we show that cl(SZ) = (2c)+ if R is not a union of less than c-many meager sets and c is a limit cardinal. If c = ω1, then cl(SZ) is equal to the bounding number of c.

The 'colour-shading effect' describes the phenomenon whereby chromatic variations affect the magnitude of perceived shape-from-shading in luminance patterns. A previous study showed that in mixed colour-plus-luminance sine-wave plaids, impressions of depth in the luminance component were enhanced by non-aligned chromatic components, and suppressed by aligned chromatic components [Nature Neurosc...

Suprathreshold binocular contrast interactions were studied psychophysically. A split-screen CRT display was used to present separate sine-wave gratings to the observer's left and right eyes. The method of constant stimuli and a modified method of adjustment were used to find sets of binocular test patterns that matched a given binocular standard. Test patterns consisted of the simultaneous pre...