Vraja/Braj

Vraja is an old Sanskrit word that is now used to denote “Braj,” or the Braj region. Vraja/Braj/Brij presently denotes a particular geographical area in and around Mathura that is related to the childhood activities of Krishna (Skt. Kṛṣṇa), the most popular incarnation (avatar) of Lord Vishnu (Skt.Viṣṇu)—so important, in fact, that some of his most influential devotees consider that he is “God himself” (bhagavān svayam), as the Bhāgavata Purāṇa declares. The word vraja is derived from the Sanskrit verbal root dhātu (vraj), which means “go, walk, proceed,” implying “motion and movement.” In its early forms it can be used to designate areas where cows graze, but it may also refer to a cow pen or cattle shed. More broadly, it has to do with the culture of a semi-nomadic pastoral encampment. The modern-day term Braj, building on these meanings, denotes a conceptual as well as a geographic entity—the former related to the childhood of Krishna, the latter to the area on the banks of the River Yamuna where he is considered to have spent his childhood and youth. The language associated with this region is Brajbhasha [Skt.Brajbhāṣā], which came to have an almost canonical weight—along with Persian and Sanskrit—in Mughal times; for that reason, along with others, it came to be well known far beyond the geographical area of Braj itself. By no means is every usage of Brajbhasha to be associated with Krishna, although his imprint is often to be felt. Over the long course of time, then, we have, on the one hand, a sedimentation and localization of the term vraja (its geographical usage), and, on the other, an expansion of the term (its conceptual breadth and linguistic weight). Acknowledgement: Dr. John Stratton Hawley helped edit this article.

Penguasaan 4 (Empat) Prasyarat Dasar Aritmatika untuk Meningkatkan Kemampuan Siswa Sekolah Dasar dalam Menyelesaikan Soal Matematika

The purpose of this study discusses how mastery of 4 (four) basic prerequisites of arithmetic which includes the ability to count, make Arithmetic / multiples, complement especially Nines and ten, and the concept of place values in numbers affect students' ability to solve math problems consisting of addition, subtraction, multiplication, and multiplication. The approach in this study uses a descriptive approach, the method used is a combination of qualitative and quantitative methods. A qualitative approach is used to describe the basic arithmetic mastery of students including numeracy, making Arithmetic / multiples numbers, complements especially nines and ten, and the concept of place values in numbers. The quantitative approach uses statistical tests with canonical correlation analysis to answer the relationship and influence between understanding of basic arithmetic mastery on the ability to solve math problems related to addition, subtraction, multiplication and division. From the results of the canonical weight and canonical loading function 1, it can be concluded that there is indeed a significant relationship between the dependent variate and the independent variate or basic arithmetic mastery and the students' ability to do math problems is indeed correlated together.

A Jacobi–Davidson Method for Large Scale Canonical Correlation Analysis

In the large scale canonical correlation analysis arising from multi-view learning applications, one needs to compute canonical weight vectors corresponding to a few of largest canonical correlations. For such a task, we propose a Jacobi–Davidson type algorithm to calculate canonical weight vectors by transforming it into the so-called canonical correlation generalized eigenvalue problem. Convergence results are established and reveal the accuracy of the approximate canonical weight vectors. Numerical examples are presented to support the effectiveness of the proposed method.

Big Galois representations and -adic -functions

Let$p\geqslant 5$be a prime. If an irreducible component of the spectrum of the ‘big’ ordinary Hecke algebra does not have complex multiplication, under mild assumptions, we prove that the image of its Galois representation contains, up to finite error, a principal congruence subgroup${\rm\Gamma}(L)$of$\text{SL}_{2}(\mathbb{Z}_{p}[[T]])$for a principal ideal$(L)\neq 0$of$\mathbb{Z}_{p}[[T]]$for the canonical ‘weight’ variable$t=1+T$. If$L\notin {\rm\Lambda}^{\times }$, the power series$L$is proven to be a factor of the Kubota–Leopoldt$p$-adic$L$-function or of the square of the anticyclotomic Katz$p$-adic$L$-function or a power of$(t^{p^{m}}-1)$.

The Structure of Performance of a Sport Rock Climber

This study is a contribution to the discussion about the structure of performance of sport rock climbers. Because of the complex and multifaceted nature of this sport, multivariate statistics were applied in the study. The subjects included thirty experienced sport climbers. Forty three variables were scrutinised, namely somatic characteristics, specific physical fitness, coordination abilities, aerobic and anaerobic power, technical and tactical skills, mental characteristics, as well as 2 variables describing the climber’s performance in the OS (Max OS) and RP style (Max RP). The results show that for training effectiveness of advanced climbers to be thoroughly analysed and examined, tests assessing their physical, technical and mental characteristics are necessary. The three sets of variables used in this study explained the structure of performance similarly, but not identically (in 38, 33 and 25%, respectively). They were also complementary to around 30% of the variance. The overall performance capacity of a sport rock climber (Max OS and Max RP) was also evaluated in the study. The canonical weights of the dominant first canonical root were 0.554 and 0.512 for Max OS and Max RP, respectively. Despite the differences between the two styles of climbing, seven variables - the maximal relative strength of the fingers (canonical weight = 0.490), mental endurance (one of scales : The Formal Characteristics of Behaviour-Temperament Inventory (FCB-TI; Strelau and Zawadzki, 1995)) (-0.410), climbing technique (0.370), isometric endurance of the fingers (0.340), the number of errors in the complex reaction time test (- 0.319), the ape index (-0.319) and oxygen uptake during arm work at the anaerobic threshold (0.254) were found to explain 77% of performance capacity common to the two styles.

The left Hilbert algebra associated to a semi-direct product

Let A and G be locally compact groups and α a continuous action of G on A, and let denote the semi-direct product of A and G. Then we prove that the left Hilbert algebra of continuous functions with compact support, has the same achieved left Hilbert algebra, as the crossed product of K(A)" by the associated action α̃ of G on . As a consequence we obtain that the canonical weight on is the dual weight of the canonical weight on K(A)".