In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Th...

This paper presents a linkage factors synthesis and multi-level optimization technique for bi-stable compliant mechanism. The linkage synthesis problem is modeled as multiple level factors and responses optimization problem with constraints. The bi-stable compliant mechanism is modeled as a crank slider mechanism using pseudo-rigid-body model (PRBM). The model exerts the large deflection of fle...

We study a class of semihomogeneous vector bundles over the product of an abelian variety and its dual. For abelian surfaces, we connect these semihomogeneous bundles to the Verlinde bundles of generalized theta functions constructed from the moduli spaces of sheaves.

In this article, Ramanujan defined am,n[3], Dharmendra. B. N and S. Vasanth Kumar Em,n[5] for any positive real numbersm n involving Ramanujan’s product of theta-functions. We established new relation between am,n Em,n explicit evaluations Em,n.

The bc-system of higher rank introduced recently is examined further. Its correlation functions are expressed through certain non-Abelian theta-functions and it is shown how quasideterminants arise. The associated U(1)-current is described geometrically and some local computations for the operator product expansions are made.

to add 1. Curious q-series Identities Since Rogers [32] introduced the false theta functions, they have played a curious role in the theory of partitions (see for instance [1, 2, 12]). Andrews [3] defined a false theta function as any series of the shape ∑ n∈Z(±1)q 2+`n that has different signs for the nonzero terms. For example, Rogers proved (1.1) ∑ j≥0 q j(3j+1) 2 − ∑ j≤−1 q j(3j+1) 2 = ∑ j≥...

485–7. 3. Lo YMD, Tein MS, Lau TK, Haines CJ, Leung TN, Poon PM, et al. Quantitative analysis of fetal DNA in maternal plasma and serum: implications for noninvasive prenatal diagnosis. Am J Hum Genet 1998;62:768–75. 4. Zhong XY, Laivuori H, Livingston JC, Ylikorkala O, Sibai BM, Holzgreve W, et al. Elevation of both maternal and fetal extracellular circulating deoxyribonucleic acid concentrati...

Leg 135 of the Ocean Drilling Program drilled and cored eight sites across the Lau Basin and adjacent Tonga Ridge to study the geological evolution of a backarc basin and adjacent oceanic arc and forearc. Six sites (Sites 834, 835, 836, 837, 838, and 839) were drilled within the Lau Basin, each within smaller and narrower (<10 km) north-south fault basins and collectively representing a broad e...

Recently, T. Bridgeland defined a complex hyperkähler metric on the tangent bundle over space of stability conditions triangulated category, based Riemann–Hilbert problem determined by Donaldson–Thomas invariants. This is encoded in function $$W(z,\theta )$$ satisfying heavenly equation, or potential $$F(z,\theta an isomonodromy equation. After recasting RH into system TBA-type equations, we ob...

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the multiplicative periods. This paper shows that for a certain subclass of period lattices (compatible with the quantization form), quantum thetas satisfy an analog of ano...