A Note on Quartic Diophantine equation X4−Y4=R2−S2X^4-Y^4=R^2-S^2

In this paper, we deal with the quartic Diophantine equation $X^4-Y^4=R^2-S^2$ to present its infinitely many integer solutions

A SURVEY ON CHURN ANALYSIS AND PREDICTION IN VIDEO ON DEMAND

Consumer loyalty is a key measure of achievement. Despondent clients will not be staying around the service. When there are unhappy clients once in a while voice their disappointment before leaving. Streaming administration, motion pictures, and television shows are gushing over the internet, not being downloaded, so we should be associated with the internet all through your watch instantly experience. Hence, to help them recognize to disappointed clients†from the get-go in their relationship. Doing as such would permit streaming administration to find a way to enhance client's joy†before it's excessively late. To distinguish the purposes behind clients who are producing from the spilling administration furthermore anticipating what number of clients will get stick around the gushing administration.Â

Iodidotris(triphenyl­phosphine)copper(I) acetonitrile solvate

The title compound, [CuI(C18H15P)3]·C2H3N, was obtained from the reaction of triphenyl­phosphine and copper(I) iodide in acetonitrile. The monomeric form of the complex has slightly distorted coordination of Cu by the I atom and three P atoms. The crystal structure is stabilized by C—H⋯π inter­actions between phenyl H atoms and phenyl rings. In addition, the complex mol­ecules exhibit C—H⋯N hydrogen bonds between phenyl H atoms and acetonitrile N atoms. The crystal used was an inversion twin, with nearly equal component populations of 0.522 (8) and 0.478 (8)

PAC-learning is Undecidable

The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the existence of a test or criterion for deciding the feasibility of attempting to learn. We investigate the existence of such a criterion in the setting of PAC-learning, basing the feasibility solely on whether the mapping to be learnt lends itself to approximation by a given class of hypothesis functions. We show that no such criterion exists, exposing a fundamental limitation in the decidability of learning. In other words, we prove that testing for PAC-learnability is undecidable in the Turing sense. We also briefly discuss some of the probable implications of this result to the current practice of machine learning

Chlorido(1-cyclo­pentyl­idene-4-ethyl­thio­semicarbazidato-κ2 N 1,S)diphenyl­tin(IV)

The Sn atom in the title compound, [Sn(C6H5)2(C8H14N3S)Cl], is penta­coordinated with a trigonal-bipyramidal coordination geometry. The 1-cyclo­pentyl­idene-4-ethyl­thio­semicarbazidate (cpetsc) ligand coordinates through the S atom and the N atom bonds to the cyclo­pentyl group, forming a five-membered ring with the Sn center. The chloride ligand and the coordinated N atom are in axial positions. In the crystal structure, inter­molecular N—H⋯Cl hydrogen bonds form chains along [101]

Effectiveness of static bicycle on improving paediatric endurance in spastic diplegic cerebral palsy children

INTRODUCTION : Spastic diplegia ‘s particular type of brain damage inhibits the proper development of upper motor neuron function,impacting the motor cortex,the basal ganglia and the corticospinal tract.This abnormally high muscle tone that results creates life long difficulty with all voluntary and passive movement in the legs and in general creates stress over time.Constant spasticity ultimately produces pain,muscle/joint break down. OBJECTIVE : It is an experimental study design to determine the effectiveness of static bicycle on improving pediatric endurance n spastic diplegic cerebral palsy children. DESIGN: The study was Pre-test and post-test experimental group design. PARTICIPANTS : A sample of 40 spastic diplegic cerebral palsy children were divided in to 2 groups : Group A :Experimental group :Treated with static bicycle Group B : Control group treated with traditional stretching and mat activities. OUTCOME MEASURES : Pediatric endurance was measured using 600-yard walk run test and 30 sec walk test. RESULTS : Statistically group A was significant when compared to group B which received stationary bicycle. CONCLUSION : The study concludes that stationary bicycling in beneficial in improving paediatric endurance in patients with spastic diplegic cerebral palsy.Thus, this study accepts the alternate hypothesis

Chloridodiphen­yl{[1-(1,3-thia­zol-2-yl-κN)ethyl­idene]-4-phenyl­thio­semicarbazidato-κ2 N 1,S}tin(IV) methanol monosolvate

The title compound, [Sn(C6H5)2(C12H11N4S2)Cl]·CH4O, is formed during the reaction between 2-acetyl­thia­zole 4-phenyl­thio­semicarbazone (Hacthptsc) and diphenyl­tin(IV) dichloride in methanol. In the crystal structure, the Sn atom exhibits an octa­hedral geometry with the [N2S] anionic tridentate thio­semicarbazone ligand having chloride trans to the central N and the two phenyl groups trans to each other. The Sn—Cl distance is 2.5929 (6), Sn—S is 2.4896 (6) and Sn—N to the central N is 2.3220 (16) Å. The MeOH mol­ecules link the Sn complexes into one-dimensional chains via N—H⋯O and O—H⋯Cl hydrogen bonds

Relativistic spin precession in the binary PSR J1141−-6545

PSR J1141$-$6545 is a precessing binary pulsar that has the rare potential to reveal the two-dimensional structure of a non-recycled pulsar emission cone. It has undergone $\sim 25 \deg$ of relativistic spin precession in the $\sim18$ years since its discovery. In this paper, we present a detailed Bayesian analysis of the precessional evolution of the width of the total intensity profile, to understand the changes to the line-of-sight impact angle ($\beta$) of the pulsar using four different physically motivated prior distribution models. Although we cannot statistically differentiate between the models with confidence, the temporal evolution of the linear and circular polarisations strongly argue that our line-of-sight crossed the magnetic pole around MJD 54000 and that only two models remain viable. For both these models, it appears likely that the pulsar will precess out of our line-of-sight in the next $3-5$ years, assuming a simple beam geometry. Marginalising over $\beta$ suggests that the pulsar is a near-orthogonal rotator and provides the first polarization-independent estimate of the scale factor ($\mathbb{A}$) that relates the pulsar beam opening angle ($\rho$) to its rotational period ($P$) as $\rho = \mathbb{A}P^{-0.5}$ : we find it to be $> 6 \rm~deg~s^{0.5}$ at 1.4 GHz with 99\% confidence. If all pulsars emit from opposite poles of a dipolar magnetic field with comparable brightness, we might expect to see evidence of an interpulse arising in PSR J1141$-$6545, unless the emission is patchy.Comment: Accepted for publication in Astrophysical Journal Letter

A report on rare occurrence of a mushroom coral, Cycloseris cyclolites (Lamarck, 1801) in Gulf of Mannar, India

333-334The frequent heavy–scale climatic oscillations and the recent local disturbances on the reefs worldwide were a menace for biodiversity sustenance. The major concern is that many species of Scleractinian corals could have been lost while being unaware of their existence. The recent survey yielded Cycloseris cyclolites after 29 years in the reef areas of the Gulf of Mannar Marine National Park