Concurrent multiresponse non-linear screening: Robust profiling of webpage performance

Profiling engineered data with robust mining methods continues attracting attention in knowledge engineering systems. The purpose of this article is to propose a simple technique that deals with non-linear multi-factorial multi-characteristic screening suitable for knowledge discovery studies. The method is designed to proactively seek and quantify significant information content in engineered mini-datasets. This is achieved by deploying replicated fractional-factorial sampling schemes. Compiled multi-response data are converted to a single master-response effectuated by a series of distribution-free transformations and multi-compressed data fusions. The resulting amalgamated master response is deciphered by non-linear multi-factorial stealth stochastics intended for saturated schemes. The stealth properties of our method target processing datasets which might be overwhelmed by a lack of knowledge about the nature of reference distributions at play. Stealth features are triggered to overcome restrictions regarding the data normality conformance, the effect sparsity assumption and the inherent collapse of the ‘unexplainable error’ connotation in saturated arrays. The technique is showcased by profiling four ordinary controlling factors that influence webpage content performance by collecting data from a commercial browser monitoring service on a large scale web host. The examined effects are: (1) the number of Cascading Style Sheets files, (2) the number of JavaScript files, (3) the number of Image files, and (4) the Domain Name System Aliasing. The webpage performance level was screened against three popular characteristics: (1) the time to first visual, (2) the total loading time, and (3) the customer satisfaction. Our robust multi-response data mining technique is elucidated for a ten-replicate run study dictated by an L₉(3⁴) orthogonal array scheme where any uncontrolled noise embedded contribution has not been necessarily excluded.     

Boundedness of commutators on homogeneous Herz spaces

The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R ⁿ ) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels. Project supponed in pan by the National h’atural Science Foundation of China (Grant No. 19131080) and the NEDF of China.     

Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications

In this note, we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a partially ordered Banach space. In this way, the metric properties of the examined problem can be analyzed more precisely. Moreover, this approach allows us to derive from the same theorem, on the one hand, semilocal results of Kantorovich-type, and on the other hand, global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved, on the one hand, we cover a wider range of problems, and on the other hand, by choosing our operators appropriately, we can find sharper error bounds on the distances involved than before. Furthermore, we show that special cases of our results reduce to the corresponding ones already in the literature. Finally, several examples are being provided where our results compare favorably with earlier ones.     

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC