Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm

AbstractLet S={x1,…,xn} be a set of n distinct positive integers. The n×n matrix having the greatest common divisor (xi,xj) of xi and xj as its i,j-entry is called the greatest common divisor (GCD) matrix defined on S, denoted by ((xi,xj)), or abbreviated as (S). The n×n matrix (S−1)=(gij), where gij=1(xi,xj), is called the reciprocal greatest common divisor (GCD) matrix on S. In this paper, we present upper bounds for the spectral condition numbers of the reciprocal GCD matrix (S−1) and the GCD matrix (S) defined on S={1,2,…,n}, with n≥2, as a function of Euler’s ϕ function and n

On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers

In this paper, we establish several new connections between the generalizations of Fibonacci and Lucas sequences and Hessenberg determinants. We also give an interesting conjecture related to the determinant of an infinite pentadiagonal matrix with the classical Fibonacci and Gaussian Fibonacci numbers

A Note on the Solutions of Some Linear Octonionic Equations

The main concerns of this paper are the linear equations with one term and one unknown of the forms: a(xa) =r, a(xb ) = r and (ax)b =r, and the linear equations with two terms and one unknown of the forms: (ax)b +(g x)d =r and a (xb )+g (xd ) =r over the octonion field. Explicit general solutions of the equations in forms a(xa) = r, a(xb ) = r and (ax)b = r are given, and solutions of the octonionic equations form (ax)b +(g x)d = r and a (xb )+g (xd ) = r by matrix representation of octonions are derived using some particular cases. Examples of numerical equations are considered

On the Solutions of Some Linear Complex Quaternionic Equations

Some complex quaternionic equations in the type AX-XB= C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtaine

BLENDING DIFFERENT METHODOLOGIES IN THE ACTION-ORIENTED APPROACH

The goal of training social actors in language teaching set by CEFR (CoE, 2001) (Common European Framework of Reference for Languages) has shifted the ultimate goal of language teaching from training successful communicators to training social actors who have the ability to carry out social actions in and/or outside the classroom, which gave rise to a new approach called the action-oriented approach (AoA) in language teaching. One of the unique characteristics of the AoA is that it combines or blends the previous methodological matrices in coherence and synergy. While there are different definitions of blended learning in the literature, this article focuses on one version of blended learning, which is combining or blending different methodologies within the framework of the action-oriented approach (AoA).  Article visualizations

Association of SSR markers with contents of fatty acids in olive oil and genetic diversity analysis of an olive core collection

The purpose of this research was to characterize an olive core collection using some agronomic characters and simple sequence repeat (SSR) markers and to determine SSR markers associated with the content of fatty acids in olive oil. SSR marker analysis demonstrated the presence of a high amount of genetic variation between the olive cultivars analyzed. A UPGMA dendrogram demonstrated that olive cultivars did not cluster on the basis of their geographic origin. Fatty acid components of olive oil in these cultivars were determined. The results also showed that there was a great amount of variation between the olive cultivars in terms of fatty acid composition. For example, oleic acid content ranged from 57.76 to 76.9% with standard deviation of 5.10%. Significant correlations between fatty acids of olive oil were observed. For instance, a very high negative correlation (-0.812) between oleic and linoleic acids was detected. A structured association analysis between the content of fatty acids in olive oil and SSR markers was performed. STRUCTURE analysis assigned olive cultivars to two gene pools (K = 2). Assignment of olive cultivars to these gene pools was not based on geographical origin. Association between fatty acid traits and SSR markers was evaluated using the general linear model of TASSEL. Significant associations were determined between five SSR markers and stearic, oleic, linoleic, and linolenic acids of olive oil. Very high associations (P < 0.001) between ssrOeUA-DCA14 and stearic acid and between GAPU71B and oleic acid indicated that these markers could be used for marker-assisted selection in olive

Identification of molecular markers associated with fruit traits in olive and assessment of olive core collection with AFLP markers and fruit traits

The purpose of this study was to characterize olive core collection with amplified fragment length polymorphism (AFLP) markers and fruit traits and to determine AFLP markers significantly associated with these fruit characters in olive. A total of 168 polymorphic AFLP markers generated by five primer combinations and nine fruit traits were used to characterize relationships between 18 olive cultivars. Although all olive cultivars were discriminated from each other by either AFLP markers (<0.75 similarity level) or fruit traits, clustering based on the AFLP markers and fruit traits was not significantly correlated (r = 0.13). Partial clustering of olive cultivars by AFLP markers according to their geographical origin was observed. Associations of AFLP markers with fruits were determined using a multiple-regression analysis with stepwise addition of AFLP markers. Significant associations between eight AFLP markers and fruit traits were identified. While five AFLP markers demonstrated significant negative correlation with fruit and stone weight, width and length and total polyphenols (P < 0.05), three AFLP markers displayed significant positive correlation with a-tocopherol and.-tocopherol (P < 0.01). This is the first report on the association of molecular markers with fruit traits in olive. Molecular markers associated with morphological and agronomic traits could be utilized for the breeding of olive cultivars. However, the association power of these markers needs to be confirmed in larger populations, and highly correlated markers should then be converted to PCR-based DNA markers such as sequence-characterized amplified region markers for better utilization

The importance of the forest property right on forest protection

Özellikle son yıllarda hız kazanan genel kadastro çalışmalarına karşın, orman sınırlandırması ve orman kadastrosu çalışmalarındaki duyarsızlık ve teknik yetersizlikten dolayı önemli sayılabilecek miktarlarda orman alanları kaybedilmektedir. Trabzon ilinin Yeşilbük, Çakılca, Yeşilyurt, Sayvan ve Güney köylerinde kadastro çalışmaları 2000 yılından önce tamamlanmış ve yargıya intikal eden davalarla ilgili kararlar Yargıtayca onanmıştır. Söz konusu köylerde 766 sayılı tapulama yasası ve 3402 sayılı Kadastro yasası’na bağlı olarak kadastro çalışmaları gerçekleştirilmiştir. Çalışmalar sonucunda, mülkiyet anlaşmazlıklarının çözümünde farklı bilirkişi ve yargı kararları oluşmuştur. Ülkemizde orman varlığının korunması konusunda ciddi sorunlar yaşanmaktadır. Bu sorunların en önemlilerinden birisi de orman olarak nitelendirilecek yerler ve sahiplerinin belirlenmemiş olmasıdır. Bölgedeki orman kadastro çalışmalarında, geleneksel kabuller ile yasal düzenlemeler arasındaki farklılıktan kaynaklanan sorunların yanı sıra, uygulayıcıların birbiriyle tam olarak örtüşmeyen kararları da çekişmelerin artmasına neden olmaktadır. Bu uyumsuzluğun orman-halk ilişkileri üzerinde olumsuz etki yaptığı, var olan mülkiyet sorununu arttırdığı gözlenmektedir.Even this is accepted as a most important problem of forestry in this region. In spite of general land parcelling which has been accelerated especially in recent years, a considerable amount of forest area has been lost because of insensitivity and technical insufficiency in the forest boundary and forestland parcelling. Cadastral works were finished in villages of Yeşilbük, Çakılca, Yeşilyurt and Güney in Trabzon and were approved by court of appeal. This Works were applied to land at those villages with Land Registry Law No. 766 and Cadastral Law no. 5304. As a result of studies, different expert and judgment decisions were become to solve of ownership disagreement. There are serious problems in conserving of forest lands in Turkey. One of these most important problems is describing forest lands and their owners. The differences between the traditional assertions and the legitimate arrangements, and also disagreements between decisions of forests have been the cause of the increasing conflicts of the cadastral surveys carried out in this region. It has been observed that these uncongenial decisions have created some negative impacts in relationships between forest organization and public, and have increased the problems in property right

Clinical Efficacy of Low Dose Flutamide plus Diane-35 in the Treatment of Idiopathic Hirsutism and Polycystic Ovary Syndrome

Objective: Idiopathic hirsutism (IH) or polycystic ovary syndrome (PCOS) are the most common causes of hirsutism which affects 5–10 % of all women. The aim of this study was to evaluate the efficacy of flutamide plus diane 35 in the treatment of idiopathic hirsutism and polycystic ovary syndrome. Materials and Methods: 26 polycystic ovary syndrome and 24 idiopathic hirsutism patients were evaluated. Fifty patients were divided into two groups according to their diagnosis: idiopathic hirsutism or polycystic ovary syndrome. All patients received 125mg Flutamide once a day and Diane 35 tablets for 21 days of each month, for 12 months. We measured hirsutism scores and hormonal levels of all patients. Evaluations were done before treatment, in the 6th and 12th months of therapy. Results: There were no significant differences in Ferriman-Gallwey scores at the beginning and at the end of the therapy between the IH and PCOS groups. The decreases in Ferriman-Gallwey scores were significant in both groups in the 6th and 12th month of therapy. Combined treatment significantly decreased total and free testosterone, DHEAS and significantly increased SHBG levels in both groups and additionally decreased levels of LH, androstenodione and LH/FSH ratio in the polycystic ovary syndrome group. Conclusion: Combined treatment was effective and safe in the treatment of hirsutism. Combined regimens have additional effects on the treatment of hirsutism