Remarks on the rightmost critical value of the triple product L-function

Let [Formula: see text] be a normalized cuspidal Hecke eigenform. We give explicit formulas for weighted averages of the rightmost critical values of triple product [Formula: see text]-functions [Formula: see text], where [Formula: see text] and [Formula: see text] run over an orthogonal basis of [Formula: see text] consisting of normalized cuspidal Hecke eigenforms. Those explicit formulas provide us an arithmetic expression of the rightmost critical value of the individual triple product [Formula: see text]-functions.

LL (1) Parser versus GNF inducted LL (1) Parser on Arithmetic Expressions Grammar: A Comparative Study

The prime objective of the proposed study is to determine the induction of Greibach Normal Form (GNF) in Arithmetic Expression Grammars to improve the processing speed of conventional LL(1) parser. Conventional arithmetic expression grammar and its equivalent LL(1) is used in the study which is converted. A transformation method is defined which converts the selected grammar into a Greibach normal form that is further converted into a GNF based parser through a method proposed in the study. These two parsers are analyzed by considering 399 cases of arithmetic expressions. During statistical analysis, the results are initially examined with the Kolmogorov-Smirnov and Shapiro-Wilk test. The statistical significance of the proposed method is evaluated with the Mann-Whitney U test. The study described that GNF based LL(1) parser for arithmetic take fewer steps than conventional LL(1) grammar. The ranks and asymptotic significance depict that the GNF based LL(1) method is significant than the conventional LL(1) approach. The study adds to the knowledge of parsers itself, parser expression grammars (PEG’s), LL(1) grammars, Greibach Normal Form (GNF) induced grammar structure, and the induction of Arithmetic PEG’s LL(1) to GNF based grammar.

What counts? Sources of knowledge in children’s acquisition of the successor function

Although many US children can count sets by 4 years, it is not until 5½-6 years that they understand how counting relates to number - i.e., that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½-6-year-olds (N = 136) may leverage to acquire this “successor function”: (1) mastery of productive rules governing count list generation; and (2) training with “+1” math facts. Both productive counting and “+1” math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from “+1” math facts.

A Study on Misconception of Using Brackets in Arithmetic Expression

The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and algebra. If the bracket is not used properly, the value of the mathematical result is completely changed. The concept of this bracket is inserted into the students while learning school-based mathematics. So at the beginning of the bracket learning process, school-based textbooks, curriculum, and teachers are of great importance. The methodology of the proposed study is based on the document-based analysis. This study employed including studying international and national journals, library consultation, expert opinion, online journals, periodical, newspapers, and documents. Finally, the researcher suggested the importance, precaution, and effectiveness of using brackets in arithmetic.

Compaction of Church Numerals

In this study, we address the problem of compaction of Church numerals. Church numerals are unary representations of natural numbers on the scheme of lambda terms. We propose a novel decomposition scheme from a given natural number into an arithmetic expression using tetration, which enables us to obtain a compact representation of lambda terms that leads to the Church numeral of the natural number. For natural number n, we prove that the size of the lambda term obtained by the proposed method is O ( ( slog 2 n ) ( log n / log log n ) ) . Moreover, we experimentally confirmed that the proposed method outperforms binary representation of Church numerals on average, when n is less than approximately 10,000 .

An Effective Conversion Algorithm of Arithmetic Expression from Infix Form to Prefix Form

Generally, when we optimize the object code of expression in source program, we get the optimizing code in the binary tree of this expression. Expressions in source program are in infix form, while the prefix form is more efficient for the binary tree. Hence this paper is to provide an effective transition algorithm of arithmetic expression from infix form to prefix form.