Submatrices of four dimensional summability matrices

In this paper, we show that a matrix that maps ℓ′′ into ℓ′′ can be obtained from any RH-regular matrix by the deletion of rows. Also a four dimensional conservative matrix can be obtained by the deletion of rows from a matrix that preserves boundedness. We will use these techniques to derive a sufficient condition for a four dimensional matrix to sum an unbounded sequence

Multivalence of bivariate functionsof bounded index

This paper examines the relationship between the concept of bounded index and the radius of univalence, respectively p-valence, of entire bivariate functions and their partial derivatives at arbitrary points in C^2

Entire bivariate functions of exponential type

In this paper we will analysis the concepts of bivariate entire complex valued functions of exponential type. To accomplish this goal, we begin with the presentation of a notion of bounded index for bivariate complex functions. Using this notion we present a series of sufficient conditions that ensure that exponential type is preserved

Some Tauberian theorems for four-dimensional Euler and Borel summability

The four-dimensional summability methods of Euler and Borel are studied as mappings from absolutely convergent double sequences into themselves. Also some Tauberian results are proved

INCLUSION THEOREMS DOUBLE DEFERRED CESARO MEANS III

R. P. Agnew presents a definition for Deferred Cesaro mean. Using this definition R. P. Agnew presents inclusion theorems for the deferred and none Deferred Cesaro means. This paper is part III of a series of papers that present extensions to the notion of double Deferred Cesaro means. Similar to the part I [11] and  the part 2 [12] this paper uses these definitions and the notion of regularity for four-dimensional matrices, to present a multidimensional inclusion theorem and a multidimensional equivalent theorem, which are the multidimensional analog of R. P. Agnew's results in [2]

Asymptotically lacunary statistical equivalence of double sequences of sets

The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets

Automatic Ranking of Retrieval Systems in Imperfect Environments

The empirical investigation of the effectiveness of information retrieval (IR) systems requires a test collection, a set of query topics, and a set of relevance judgments made by human assessors for each query. Previous experiments show that differences in human relevance assessments do not affect the relative performance of retrieval systems. Based on this observation, we propose and evaluate a new approach to replace the human relevance judgments by an automatic method. Ranking of retrieval systems with our methodology correlates positively and significantly with that of human-based evaluations. In the experiments, we assume a Web-like imperfect environment: the indexing information for all documents is available for ranking, but some documents may not be available for retrieval. Such conditions can be due to document deletions or network problems. Our method of simulating imperfect environments can be used for Web search engine assessment and in estimating the effects of network conditions (e.g., network unreliability) on IR system performance

Effects of Estrogen Replacement Therapy on Lipid Peroxidation and Antioxidant Enzyme Activities of Ovariectomized and Ovariectomized-Diabetic Rats

Menopause and diabetes are conditions producing free radicals independently from each other. Estrogen replacement therapy which widely used in postmenopausal period has beneficial effects because of its antioxidant property. The study groups were as follows: ovariectomy (n=8), ovariectomy+17-östradiol (n=8), ovariectomy+diabetes (n=10) and ovariectomy+diabetes+17-östradiol (n=8). Diabetes was induced by streptozotocin (45 mg/kg i.p.) and the treatment with 17-östradiol (0.1 mg/kg/day) was started a week after ovariectomy. After–week long experimental period aortic and uterine tissues were collected from the animals and the malondialdehyde concentration, glutathione peroxidase and catalase activities were quantified. The treatment did not effect blood glucose concentrations, but increased plasma estradiol concentrations. Increased malondialdehyde concentrations were reduced by the treatment in aorta from diabetics and nondiabetics, but the treatment increased malondialdehyde concentrations in nondiabetic uterine while were reducing in diabetic uterine. The treatment also reduced the increased activities of catalase and glutathione peroxidase in aorta from diabetics and nondiabetics, on the other hand the treatment increased the activities of those enzymes in uterine from diabetics and nondiabetics. Our results suggested that estrogen acts as an antioxidant or prooxidant depending on the tissues