NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

In a recent paper, [1], 2005, the indefinite integrals of a certain type are calculated using some linear homogeneous differential equations of second order with variable coefficients, associated with the integrals. In some simple cases, like the examples considered in this paper, the linear independent solutions of these differential equations are directly calculated relative to elementary functions. In more difficult cases, the power series method must be used. In such situations, it is advisable to use the algebraic symbolic calculus on computer. Examples of this type will be given in a subsequent paper. Because the main formula from which the integrals can be calculated is not rigorous proved in [1], we give here a correct proof based on the Abel-Liouville formula for the differential equations of second order. For completeness, we give here the proof for this formula and some of its applications, necessary to our work. Also, we included two examples.indefinite integrals, second order linear homogeneous differential equations, Abel-Liouville formula

INITIAL AND BOUNDARY VALUE PROBLEMS FOR DIFFERENCE EQUATIONS

We consider initial and boundary value problems for linear nonhomogeneous difference equations with constant coefficients. For such problems we compute the numerical values of the solutions using the discrete deconvolution. The method can be easily used in applications and implemented on computer.difference equations, initial and boundary value problems, discrete convolution and deconvolution

LINEAR DISCRETE CONVOLUTION AND ITS INVERSE. PART 2. DECONVOLUTION

We present here several ways for calculating the linear discrete convolution and its inverse - the deconvolution, by direct methods, generator functions, Z-transform, using matrices and MATLAB. These notions was used by author in a series of papers, especially for solve several types of equations.complete and truncated linear discrete convolution and deconvolution

Translating programming languages for intermediate codes

Many of the important data structures used in a compiler are intermediate representations of the program being compiled. Often these representations take the form of trees, with several node types, each of which has different attributes. Tree representations can be described with grammars, just like programming languages. For each grammar rule, there is one constructor that belongs to the class for its left-hand-side symbol. I simply extend the abstract class with a concrete class for each grammar rule. Each grammar rule has right hand side components that must be represented in the data structures.compiler, lexical analysis, abstract syntax, intermediate representation, abstract machine language

Vulvodynia; an under-recognized disease

Vulvodynia is a chronic condition which affects an increasing number of women; it presents currently an incidence that is higher than had previously been estimated. Regarding pathogenesis, several (hormonal, infectious, inflammatory and psychological) factors have been proposed, but vulvodynia etiology remains still unclear. This disorder is a multifactorial condition with a significant impact on the patient’s quality of life, yet is difficult to diagnose (an under-estimated/ under-recognized affection). Certain medical investigations are required in order to exclude other diseases (the diagnosis of vulvodynia being one of exclusion), but anamnesis and physical examination are essential steps in the diagnosis. Although many therapies have been proposed, both pharmacological and non-pharmacological, a standardized therapy has not yet been established/ generally accepted. Accordingly, many therapeutic options have been studied with varying results. Vulvodynia remains a challenging disease and a multidisciplinary approach is needed to achieve satisfactory outcomes. Further studies are needed to completely understand its pathogenesis and to develop a standardized treatment

A certain integral-recurrence equation with discrete-continuous auto-convolution

summary:Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations

Therapeutic challenges in a case of psoriasis with nail onset

Nail psoriasis affects a large number of patients with psoriasis and has a major psychosocial impact. Furthermore, it may be regarded as a predictor of more severe forms of psoriasis and early sign of psoriatic arthritis. The clinical presentations vary depending on the structure affected (nail matrix or nail bed), the nail lesions may range from minor to severe, but they are not specific. Treatment is a challenge, in most cases the lesions being resistant to therapy. We present a rare case of psoriasis with nail onset in a 59-year-old woman. The nail involvement confined to the fingernails was severe, with significant impairment of the patient’s quality of life. Conventional therapies failed to improve the nail lesions, but a marked improvement was achieved under etanercept therapy

Diagnostic challenges and treatment difficulties in a patient with excoriated acne conglobata

Acne conglobata is a rare and severe form of acne vulgaris, characterized by the presence of comedones, papules, pustules, nodules and sometimes hematic or meliceric crusts. Acne excoriée is a form of self-inflicted skin condition in which the patient picks on imaginary or real acne lesions. We report the case of a 16 year old Caucasian female patient from the urban area who addressed our dermatology department for erythematous, edematous plaques covered by pustules and crusts, located on the face. The anamnesis revealed that during the last weeks she had had a depressive mood after ending a relationship with her boyfriend and started scratching and picking on the lesions. The patient\u27s depressive mood prior to the worsening of the disease was probably aggravated by the condition. This might have determined the picking of the skin which could have impeded the response to standard treatment. The self-excoriative behavior could also be regarded as an appeal for help