Support vector machine (SVM) is a very popular method for binary data classification in data mining (machine learning). Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of good optimal algorithms can’t be used to find the solution. In order to overcome this model’s non-smooth property, Lee and Mangasarian proposed smooth support vector machine (SSVM) i...

a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical ...

Suppose we are given a finite subset E ⊂ R and a function f : E → R. How to extend f to a C function F : R → R with C norm of the smallest possible order of magnitude? In this paper and in [20] we tackle this question from the perspective of theoretical computer science. We exhibit algorithms for constructing such an extension function F , and for computing the order of magnitude of its C norm....

The control of force production in vascular smooth muscle is critical to the normal regulation of blood flow and pressure, and altered regulation is common to diseases such as hypertension, heart failure, and ischemia. A great deal has been learned about imbalances in vasoconstrictor and vasodilator signals, e.g., angiotensin, endothelin, norepinephrine, and nitric oxide, that regulate vascular...

Smooth muscles are complex tissues containing a variety of cells in addition to muscle cells. Interstitial cells of mesenchymal origin interact with and form electrical connectivity with smooth muscle cells in many organs, and these cells provide important regulatory functions. For example, in the gastrointestinal tract, interstitial cells of Cajal (ICC) and PDGFRα(+) cells have been described,...

The sarcoplasmic reticulum (SR) of smooth muscles presents many intriguing facets and questions concerning its roles, especially as these change with development, disease, and modulation of physiological activity. The SR's function was originally perceived to be synthetic and then that of a Ca store for the contractile proteins, acting as a Ca amplification mechanism as it does in striated musc...

The gastrointestinal tract normally functions to move ingested food, in an organized fashion, from the oropharynx, through the stomach, small intestine and colon and into the rectum, from which it can be expelled. The primary function of the colon is to absorb water and electrolytes from the chyme delivered and, thus, determine the frequency, consistency, and volume of stools eliminated. The co...

Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over finite fields. Some of them have a provable subexponential running time and are using the fact that smooth reduced ideals are sufficiently dense. We explicitly show how these density results can be derived. All proofs are purely combinatorial and d...

For nonsmooth Filippov systems, the stability of system is assumed to be proved by Lyapunov functions, such as piecewise smooth functions. This extension was based on solution and Clarke generalized gradient. However, it difficult estimate gradient a non-smooth function. In some cases, can divided into continuous discontinuous components. If Lebesgue measure components zero, function utilized p...