(1 < p ≤ ∞) [LS87f]. (2) [HR88a]. (2m− 2) [KL88]. (A0, A1)θ1 [Xu87a]. (α, β) [Pie88a, Fin88a]. (d ≥ 1) [Wsc85a]. (λ) [DM85b]. (Z/2) [Car86b]. (nα) [Sch85h]. (φ)2 [BM89c]. (τ − λ)u = f [Wei87r]. (x, t) [Lum87, Lum89]. (X1 −X3, X2 −X3) [SW87]. 0 [Caz88, Kas86, Pro87]. 0 < p < 1 [Cle87]. 1 [Bak85a, DD85, Drm87, Eli88, FT88a, Gek86d, HN88, Kos86a, LT89, Pet89a, Pro87, Tan87, vdG89]. 1/4 [KS86e]. 1 ≤ q < 2 [Gue86]. 2 [BPPS87, Cam88, Cat85a, ES87b, Gan85e, Gol86a, HRL89g, Hei85, Hua86, Kan89, KB86, Li86, LT89, Mil87b, Mur85a, Qui85b, SP89, Shi85, Spe86, Wal85b, Wan86]. 2m− 2 [Kos88b]. 2m− 3 [Kos88b]. 2m− 4 [Kos88b]. 2× 2 [Vog88]. 3 [Aso89, BPPS87, BW85c, BG88b, Che86d, Fis86, Gab85, Gu87a, HLM85b, Kam89b, Kir89c, Lev85c, Mil85c, Néd86, Pet86, Ron86, Sch85b, ST88, Tur88b, Wan86, Wen85, tDP89, vdW86]. 4 [Bau88a, Don85a, FKV88, Kha88, Kir89l, SS86, Seg85b, Wal85b]. 5 [Ito89, Kir89e, SV85]. 5(4) [Cas86]. 5819539783680 [KSX87]. 6 [PH89, Žub88].

/pdf/a-complete-bibliography-of-lecture-notes-in-mathematics-1985-32lbz48rms.pdf

A Complete Bibliography of Lecture Notes in Mathematics (1985{1989)

The intent of this special issue is to extend community psychology's voice in the growing discourse about spirituality, religion, and psychology. While lively debate will continue about particular religious beliefs, the social significance of religious and spiritual experiences cannot be overlooked. These papers will not enter the debate over the existence of a higher power, but rather they will contribute to the development of knowledge and greater understanding of how these phenomena are interwoven into social life. Some authors focus on how religion and spirituality can serve as independent variables that have an impact on phenomena of interest, from the individual to the institution. In other papers, spirituality is treated more as a dependent variable, important as an outcome in its own right. In several of the papers, religion and spirituality are integral parts of an intervention. In sum, when religion and spirituality are viewed as legitimate variables of psychological study, they offer seemingly endless perspectives on human behavior. © 2001 John Wiley & Sons, Inc.

A reunion of ideas: Complementary inquiry and collaborative interventions of spirituality, religion, and psychology

Multi-valued neurons (MVNs) and universal binary neurons (UBNs) are neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by a partially-defined multiple-valued function on a single MVN, and an arbitrary mapping described by a partially-defined or fully-defined Boolean function (which does not have to be a threshold function) on a single UBN. Rapidly-converging learning algorithms exist for both types of neurons. Such features of MVNs and UBNs may be used to solve different kinds of problems. One of the most successful applications of MVNs and UBNs is their use as basic neurons in cellular neural networks (CNNs) to solve image processing and image analysis problems.

Image processing using cellular neural networks based on multi-valued and universal binary neurons

As it is known, the impulsive noise appears on the image in the form of randomly distributed pixels of random brightness. Impulses themselves usually differ much from the surrounding pixels in brightness. The main topic of the paper is the introduction of the new impulse detection criteria, and their application to such filters as median, rank-order and cellular neural Boolean. Three impulse detectors are considered. The Rank Impulse Detector uses such property of impulse that its rank in variation series is usually quite different from rank of the median. Exponential Median Detector uses the exponent of the difference between the local median and the value of pixel to detect the impulse. Combination of these two detectors forms the Enhanced Rank Impulse Detector and integrates advantages of both of them. In combination with filter it allows iterative filtering without further image destruction.

Detectors of the impulsive noise and new effective filters for the impulsive noise reduction

By using mathematical reasoning, this paper demonstrates the treatment principle: “Virtual disease is to fill his mother but real disease is to rush down his son” and “Strong inhibition of the same time, support the weak” based on “Yin Yang Wu Xing” Theory in Traditional Chinese Medicine (TCM). We defined two kinds of opposite relations and one kind of equivalence relation, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the treatment of TCM and treated the healthy body as a steady multilateral system, it has been proved that the treatment principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.

/pdf/mathematical-reasoning-of-treatment-principle-based-on-yin-3wb7yrgmbk.pdf

Mathematical Reasoning of Treatment Principle Based on “Yin Yang Wu Xing” Theory in Traditional Chinese Medicine

Nonlinear cellular neural filters (NCNF) are based on the non- linearity of the activation functions of universal binary neuron (UBN) and multi-valued neuron (MVN). NCNF, which include the multi-valued non-linear filters (MVF) and cellular Boolean filters (CBF), their applications are presented in detail in this paper. The following problems are considered in the paper: (1) NCNF in general as a class of nonlinear filters, which includes multi-valued and cellular Boolean filters based on similar complex non-linearities; (2) Multi- valued filters as a nonlinear generalization of the simple low-pass and mean filters; (3) Connection of the multi-valued filters with other nonlinear filters; (4) Cellular Boolean filters; (5) Application of the NCNF to noise reduction; (6) Application of the NCNF to the extraction of image details; (7) Application of the NCNF to precise edge detection, edge detection by narrow direction, and image segmentation.

Nonlinear cellular neural filtering for noise reduction and extraction of image details

Construction of generalized Hadamard matrices

Hadamard matrices have received much attention in recent years, owing to their numerous known and promising applications. The FHT algorithm was developed for N = 2n, 12 · 2n, 4n. In this chapter, a general and efficient algorithm to compute 4t-point (t is an "arbitrary" integer) HTs is developed. The proposed scheme requires no zero padding of the input data to make it the size equal to 2n. The difficulty of the construction of the N ≡ 0 (mod 4)-point HT is related to the Hadamard problem, namely, we do not know if, for every integer n, there is or is not an orthogonal 4n × 4n matrix of plus and minus ones. The number of real operations is reduced from O(N2) to O(N log2 N). Comparative estimates revealing the efficiency of the proposed algorithms with respect to those known are given. In particular, it is demonstrated that, in typical applications, the proposed algorithm is significantly more efficient than the conventional WHT. Note that the general algorithm is more efficient for Hadamard matrices of orders ≥96 than the classical WHT, whose order is a power of 2. The algorithm renders a simple and symmetric structure. Note that there are many approaches and algorithms concerning HTs. In this chapter, we present new algorithms for fast computation of HTs of any existing order. Additionally, using the structures of those matrices, we reduce the number of operations. The chapter is organized as follows. Section 8.1 presents three algorithms of Hadamard matrix construction. Sections 8.2 and 8.3 present the decomposition of the arbitrary Hadamard matrix by {(1, 1), (1, −1)}
and by the {(1, 1, 1, 1), (1, 1, −1, −1), (1, −1, −1, 1), (1, −1, 1, −1)} vector system. Section 8.4 describes these decompositions based on N ≡ 0 (mod 4)-point FHT algorithms. Section 8.5 describes a multiply/add instruction-based FHT algorithm that primarily uses shifted operations. Section 8.6 presents the complexity of
developed algorithms, as well as comparative estimates, revealing the efficiency of the proposed algorithms with respect to those known.

Fast Hadamard Transforms for Arbitrary Orders

Hadamard matrices have recently received attention due to their numerous known and promising applications. The FHT algorithms were developed for the orders N = 2n, 12 · 2n, 4n. The difficulties of the construction of the N ≡ 0(mod 4)-point HT are related to the problem of the existence of Hadamard matrices (the so-called
Hadamard problem). In this chapter, we have utilized a Williamson's construction of parametric Hadamard matrices in order to develop efficient computational algorithms of a special type of HTs-the Williamson-Hadamard transforms. Several algorithms for fast computation of a special type of HTs, namely, the Williamson-Hadamard transform, are presented. An efficient algorithm to compute 4t-point (t is an "arbitrary" integer number) Williamson-Hadamard transforms is traced. Comparative estimates revealing the efficiency of the proposed algorithms with respect to ones known are given, and the results of numerical examples are presented. Section 5.1 describes the Hadamard matrix construction from Williamson matrices. Sections 5.2 and 5.3 present the block representation of parametric Williamson-Hadamard matrices and the fast Williamson-Hadamard block transform algorithm. In Section 5.4, the Williamson-Hadamard transform algorithm on add/shift architecture is developed. Sections 5.5 and 5.6 present fast
Williamson-Hadamard transform algorithms based on multiplicative theorems. In Section 5.7, complexities of developed algorithms and also comparative estimates are presented, revealing the efficiency of the proposed algorithms with respect to ones known.

Fast Williamson-Hadamard Transforms

Skew Hadamard matrices are of special interest due to their uses, among others, in constructing orthogonal designs. Fast computational algorithms for skew Williamson-Hadamard transforms are constructed in this chapter. Fast algorithms of two groups of transforms based on skew-symmetric Williamson-Hadamard matrices are designed using the block structures of these matrices. 6.1 Skew Hadamard Matrices Many constructions of Hadamard matrices are known, but not all of them give skew Hadamard matrices. In Ref. 1, the authors provide a survey on the existence and equivalence of skew-Hadamard matrices. In addition, they present some new skew Hadamard matrices of order 52 and improve the known lower bound on the number of the skew Hadamard matrices of this order. As of August 2006, skew Hadamard
matrices were known to exist for all n ≤ 188 with n divisible by 4. The survey of known results about skew-Hadamard matrices is given in Ref. 33. It is conjectured that skew Hadamard matrices exist for n = 1, 2 and all n divisible by 4. Definition 6.1.1: A matrix Am is called symmetric if ATm = Am. Matrix Am of order m is called skew symmetric if ATm = −Am. The following matrices are examples of skew-symmetric matrices of order 2, 3, and 4: (6.1) 6.1.1 Properties of the skew-symmetric matrices • If A = (ai,j) is a skew-symmetric matrix, then ai,j = 0. • If A = (ai,j) is a skew-symmetric matrix, then ai,j = −ai,j. • Sums and scalar products of skew-symmetric matrices are again skew symmetric, i.e., A and B are skew-symmetric matrices of the same orders, and c is the scalar number, then A + B and cA are skew-symmetric matrices. • If A is a skew-symmetric matrix of order n, the determinant of A satisfies det(A) = det(AT) = det(−A) = (−1)n det(A).

Sos S. Agaian

Papers

Nonlinear cellular neural filtering for noise reduction and extraction of image details

Construction of generalized Hadamard matrices

Fast Hadamard Transforms for Arbitrary Orders

Fast Williamson-Hadamard Transforms

Skew Williamson-Hadamard Transforms