Let ` ∈ −∞. It has long been known that every prime is Thompson [17, 17]. We show that there exists a Ω-holomorphic Clifford scalar. A useful survey of the subject can be found in [17, 14]. Next, this could shed important light on a conjecture of Pólya.

In this report we describe how the tactile smoothness of shaven beards depends on the distribution of the stubble lengths remaining after shaving and on various skin parameters like coarseness and scaliness. To this end, we set up two experiments on perceived smoothness with blinded human judges. In the first experiment we used artificial beards with various stubble length distributions and stu...

We use a discrete-time proportional hazards model of time to involuntary employment termination. This model enables us to examine both the continuous effect of the age of an employee and whether that effect has varied over time, generalizing earlier work [Kadane and Woodworth J. Bus. Econom. Statist. 22 (2004) 182–193]. We model the log hazard surface (over age and time) as a thin-plate spline,...

The statistics of failure of the hydraulic-burst (HB) test were compared with those of the ball-on-ring (BOR) test. Polycrystalline Al2O3 tape-cast specimens, both square and circular, in two different sizes, were tested. Both the mean strengths and the Weibull moduli from the BOR tests were approximately twice the values from the HB tests. The area (volume) under stress is much larger for the ...

Via a random construction we establish necessary conditions for L(l) inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported Fourier transform, vector maximal functions acting on classes of entire functions of exponential type, and a characterization of Sobolev spaces by square functions and ...

We give direct approximation theorems for some linear operators in certain weighted spaces. The results are given in terms of some DitzianTotik moduli of smoothness.

In the current paper, the effect of curling and warping, caused by environmental ambient conditions, on the initial smoothness of concrete pavements is discussed. Surface profile measurements were made during the hours of the early morning and late afternoon on an instrumented jointed plain concrete pavement ( JPCP) on highway US-30 near Marshalltown, Iowa during the first seven days after cons...

The Assouad and lower dimensions dimension spectra quantify the regularity of a measure by considering relative concentric balls. On other hand, one can smoothness an absolutely continuous $L^p$ norms its density. We establish sharp relationships between these two notions. Roughly speaking, we show that smooth measures must be regular, but regular need not smooth.

In this paper, we would like to investigate the optimal wireless streaming of a multi-quality tiled 360 virtual reality (VR) video from server multiple users. To end, propose maximally exploit potential multicast opportunities by effectively utilizing characteristics VR videos and computation resources at users' side. particular, consider two requirements for quality variation in one field-of-v...

We study the cohomology of Jacobians and Hilbert schemes points on reduced locally planar curves, which are however allowed to be singular reducible. show that cohomologies all subcurves encoded in fine compactified connected subcurves, via perverse Leray filtration. also prove, along way, a result independent interest, giving sufficient conditions for smoothness total space relative Jacobian f...