In this article, we shall prove a result which enables us to transfer from finite infinite Euler products. As an example, give two new proofs of the product for sine function depending on certain decompositions. We then some equivalent expressions functional equation, i.e. partial fraction expansion and integral expression involving generating Bernoulli numbers. The equivalence functions hyperb...

Many acoustic instruments create a harmonic series, a collection of sine-waves uniformly spaced in frequency. A listener aggregates such collections of sine-waves, or partials, into a single pitch. Some acoustic instruments allow portamento, the smooth glide from one pitch to another. For example, the violin and trombone. During acoustic portamento, each sine-wave transitions in parallel motion...

Phosphorylation of myosin regulatory light chain (R-LC) is associated with potentiated work and power during twitch afterloaded contractions in mouse extensor digitorum longus muscle [R. W. Grange, C. R. Cory, R. Vandenboom, and M. E. Houston. Am. J. Physiol. 269 (Cell Physiol. 38): C713-C724, 1995]. We now describe the association between R-LC phosphorylation and potentiated concentric work wh...

The proopiomelanocortin gene (POMC) is expressed in the pituitary gland and the ventral hypothalamus of all jawed vertebrates, producing several bioactive peptides that function as peripheral hormones or central neuropeptides, respectively. We have recently determined that mouse and human POMC expression in the hypothalamus is conferred by the action of two 5' distal and unrelated enhancers, nP...

This is a preprint for Max-Planck Institute’s proceedings. We present recent results in the area of unprovability. We find unprovable statements about a general class of functions using similtaneous diophantine approximation, unprovability results about the Riemann zeta-function using almost-periodicity and probabilistic arguments and a simple unprovability result about converging series using ...

The purpose of this study was to develop a method of quantifying the degree of optic disc tilt in normal eyes. This was a prospective, observational cross sectional study of 126 right eyes of 126 healthy volunteers. The optic disc tilt was determined from the circular peripapillary optical coherence tomographic (OCT) scan images. The course of the retinal pigment epithelium (RPE) layer in the p...

Height is one of the most important dimensions of trees, but few observers are fully aware of the consequences of the misapplication of conventional height measurement techniques. A new approach, the sine method, can improve height measurement by being less sensitive to the requirements of conventional techniques (similar triangles and the tangent method). We studied the sine method through a c...

This paper presents the preliminary results of an extensive parametric study on seismic response of two-dimensional semi-sine shaped hills to vertically propagating incident P- and SV-waves. Clear perspectives of the induced diffraction and amplification patterns are given by investigation of time-domain and frequency-domain responses. It is shown that site geometry, wave characteristics , and ...

Abstract. We consider Linsker’s neural network model, in particular, development of oriented receptive fields of cells on layer G, and investigate which features in this model are crucial for the development. We assume that the correlation function is a Mexican-hat shape function while we introduce the arbor function explicitly and discuss its role in the development. We compute the Fourier tra...

this paper presents a modified 32-bit rom-based direct digital frequency synthesizer (ddfs). maximum output frequency of the ddfs is limited by the structure of the accumulator used in the ddfs architecture. the hierarchical pipeline accumulator (hpa) presented in this paper has less propagation delay time rather than the conventional structures. therefore, it results in both higher maximum ope...