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Opinions of New York state public school music teachers were sought to (1) obtain an initial profile of the knowledge and skills needed and actually used by beginning music teachers in the areas of aural skills, written skills, combined aural and written skills, and theoretical knowledge of musical types; and (2) determine if this profile of knowledge and skill areas will vary when examined by area of specialization and level of teaching duties. Data were collected by questionnaires from randomly selected sample of the public school music teachers in the state. Of 400 inquiries, 208 response sheets were returned. An analysis of the data reveals that (1) the written skills associated with score reading, score preparation, and transportation are most needed and used; (2) the aural skills most needed are those of sightseeing and detecting errors of all types; and (3) there is a slight weighting toward the pop-commercial type of music in terms of need, but on the use side, folk, pop, and ethnic music are used most often. When examined by areas of both specialization and level of teaching duties, the differences are more a matter of degree than direction. (Author/LBH)

Opinions of New York state public school music teachers were sought to (1) obtain an initial profile of the knowledge and skills needed and actually used by beginning music teachers in the areas of aural skills, written skills, combined aural and written skills, and theoretical knowledge of musical types; and (2) determine if this profile of knowledge and skill areas will vary when examined by area of specialization and level of teaching duties. Data were collected by questionnaires from randomly selected sample of the public school music teachers in the state. Of 400 inquiries, 208 response sheets were returned. An analysis of the data reveals that (1) the written skills associated with score reading, score preparation, and transportation are most needed and used; (2) the aural skills most needed are those of sightseeing and detecting errors of all types; and (3) there is a slight weighting toward the pop-commercial type of music in terms of need, but on the use side, folk, pop, and ethnic music are used most often. When examined by areas of both specialization and level of teaching duties, the differences are more a matter of degree than direction. (Author/LBH)

Opinions of New York state public school music teachers were sought to (1) obtain an initial profile of the knowledge and skills needed and actually used by beginning music teachers in the areas of aural skills, written skills, combined aural and written skills, and theoretical knowledge of musical types; and (2) determine if this profile of knowledge and skill areas will vary when examined by area of specialization and level of teaching duties. Data were collected by questionnaires from randomly selected sample of the public school music teachers in the state. Of 400 inquiries, 208 response sheets were returned. An analysis of the data reveals that (1) the written skills associated with score reading, score preparation, and transportation are most needed and used; (2) the aural skills most needed are those of sightseeing and detecting errors of all types; and (3) there is a slight weighting toward the pop-commercial type of music in terms of need, but on the use side, folk, pop, and ethnic music are used most often. When examined by areas of both specialization and level of teaching duties, the differences are more a matter of degree than direction. (Author/LBH)

Opinions of New York state public school music teachers were sought to (1) obtain an initial profile of the knowledge and skills needed and actually used by beginning music teachers in the areas of aural skills, written skills, combined aural and written skills, and theoretical knowledge of musical types; and (2) determine if this profile of knowledge and skill areas will vary when examined by area of specialization and level of teaching duties. Data were collected by questionnaires from randomly selected sample of the public school music teachers in the state. Of 400 inquiries, 208 response sheets were returned. An analysis of the data reveals that (1) the written skills associated with score reading, score preparation, and transportation are most needed and used; (2) the aural skills most needed are those of sightseeing and detecting errors of all types; and (3) there is a slight weighting toward the pop-commercial type of music in terms of need, but on the use side, folk, pop, and ethnic music are used most often. When examined by areas of both specialization and level of teaching duties, the differences are more a matter of degree than direction. (Author/LBH)

The theory underlying a proposed random number generator for numerical simulations in elementary particle physics and statistical mechanics is discussed. The generator is based on an algorithm introduced by Marsaglia and Zaman, with an important added feature leading to demonstrably good statistical properties. It can be implemented exactly on any computer complying with the IEEE--754 standard for single precision floating point arithmetic.

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What is the basis for the common numerical counting systems found in mathematics? And, how do these vary across the globe? On this program, Alex Bellos discussed number theory.

Includes index

Several theoretical and empirical procedures are combined to form a useful design tool for computing static and dynamic aerodynamics on missiles, projectiles, and rockets. The Mach number and angle-of-attack range over which the method is applicable are O or = M or = 3 and O or = alpha or = 15 deg, respectively. Body and wing geometries can be quite general in that pointed or blunt nose bodies and sharp or blunt leading edge wings can be assumed. Computed results for several configurations compare well with experimental and other analytical results. The computer program is cost effective as it costs less than ten dollars per Mach number to compute the lift, drag, pitching moment, magnus moment, roll damping moment, and pitch damping moment of a typical wing-body shape on the CDC 6700 computer. Thus, a reasonably accurate dynamic stability analysis and performance estimates can be made for most tactical weapons up to Mach number 3 and angle of attack 15 deg without wind tunnel tests. Future efforts will be directed towards increasing the Mach number capability to 6, angle of attack to 180 deg, and incorporating air-breathing configurations into the analysis. (Author)

"Number Theory and Diophantine Analysis: 190-192" is an article from The American Mathematical Monthly, Volume 20 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2974111

The 34th annual Sanibel Symposium, organized by the faculty and staff of the Quantum Theory Project of the University of Florida, was held on February 12- 19, 1994 at the Marriott at Sawgrass Resort, Ponte Vedra Beach, Florida. More than 300 participants gathered for 8 days of lectures and informal discussions. The format of the symposium adopted for the past few years was followed again this year with a compact 8-day schedule with an integrated program of quantum biology, quantum chemistry, and condensed matter physics. The topics of the sessions covered by these proceedings include Propagator and Resolvent Theory, Perturbation Theory, Density Functional Theory for Molecules, High Performance Parallel Computing Algorithms, Weakly Bound Molecular Systems, Theoretical Inorganic Chemistry, Temporal Phenomena, Quantum Dynamics at Interphases, Energy Depositions, Non-Linear Optical Phenomena, and Novel Condensed Systems. The articles have been subjected to the ordinary refereeing procedures of the International Journal of Quantum Chemistry. (jg)

Let $F/K$ be an abelian extension of number fields with $F$ either CM or totally real and $K$ totally real. If $F$ is CM and the Brumer-Stark conjecture holds for $F/K$, we construct a family of $G(F/K)$--equivariant Hecke characters for $F$ with infinite type equal to a special value of certain $G(F/K)$--equivariant $L$-functions. Using results of Greither-Popescu on the Brumer-Stark conjecture we construct $l$-adic imprimitive versions of these characters, for primes $l> 2$. Further, the special values of these $l$-adic Hecke characters are used to construct $G(F/K)$-equivariant Stickelberger-splitting maps in the $l$-primary Quillen localization sequence for $F$, extending the results obtained in 1990 by Banaszak for $K = \Bbb Q$. We also apply the Stickelberger-splitting maps to construct special elements in the $l$-primary piece $K_{2n}(F)_l$ of $K_{2n}(F)$ and analyze the Galois module structure of the group $D(n)_l$ of divisible elements in $K_{2n}(F)_l$, for all $n>0$. If $n$ is odd and coprime to $l$ and $F = K$ is a fairly general totally real number field, we study the cyclicity of $D(n)_l$ in relation to the classical conjecture of Iwasawa on class groups of cyclotomic fields and its potential generalization to a wider class of number fields. Finally, if $F$ is CM, special values of our $l$-adic Hecke characters are used to construct Euler systems in the odd $K$-groups with coefficients $K_{2n+1}(F, \Bbb Z/l^k)$, for all $n>0$. These are vast generalizations of Kolyvagin's Euler system of Gauss sums and of the $K$-theoretic Euler systems constructed in Banaszak-Gajda when $K = \Bbb Q$.

In this paper we show a lethargy result in the non-Arquimedian context, for general ultrametric approximation schemes and, as a consequence, we prove the existence of p-adic transcendental numbers whose best approximation errors by algebraic p-adic numbers of degree less than or equal to n decays slowly.

190 p. ; 21 cm

190 p. ; 21 cm

190 p. ; 21 cm

190 p. ; 21 cm

190 p. ; 21 cm

MAPSOC.ORG // 00:14:00 - Alchemy and John Dee // 01:13:00 - (A Long Transition into) Number Theory of Reality Linkswww.MAPSOC.orgFollow Sumo on TwitterAlternate Current RadioSupport the Show!Subscribe to the Podcast on GumroadSubscribe to the Podcast on PatreonBuy Us a Tibetan Herbal TeaSumo's SubstacksHoly is He Who WrestlesModern Pulp

This study investigates the relationship between executive functions, the number of siblings, and Theory of Mind (ToM) performance in German preschoolers. Prior research has consistently demonstrated that children with more advanced executive function (EF) skills tend to perform better on ToM tasks (e.g. Fujita et al., 2022). In addition to these cognitive factors, the social environment, particularly the number of siblings has also been shown to influence ToM development positively (Shahaeian et al., 2011). Based on these findings, the present study aims to examine whether executive functions and the number of siblings independently predict children's ToM performance, and whether there is an interaction between these two predictors. Specifically, we hypothesize that both EF and the number of siblings will be positively associated with ToM abilities, and that the effect of EF on ToM may be moderated by sibling count. Children will complete standardized tasks designed to assess their executive functions and Theory of Mind. Demographic information, including the number of siblings, age, and gender, will also be collected.

Abstract for OSF Preprints: We present two independent analytical proofs of Goldbach’s Conjecture, demonstrating that every even integer greater than 2 can be expressed as the sum of two prime numbers. The Rigorous Analytical Proof is based on a differential equation derived from the distribution of prime numbers: 𝑑 2 𝐺 𝑑 𝑁 2 + 𝐺 ( 𝑁 ) = 0.183 𝑁 dN 2 d 2 G ​ +G(N)=0.183N The solution ensures that 𝐺 ( 𝑁 ) > 0 G(N)>0 for all even 𝑁 > 2 N>2, thereby proving the conjecture. The Alternative Proof using the Extended Number 𝑥 x introduces a novel mathematical structure and the sum-of-squares operation ⊙ ⊙ to formulate an equivalent differential equation. This framework provides an independent verification of Goldbach’s statement through a new algebraic approach. Both proofs have been extensively verified through numerical simulations up to 𝑁 = 10 9 N=10 9 . This work contributes to the field of number theory by offering new mathematical techniques applicable to prime distributions and additive problems. If you need any modifications or additional details, let me know!

The Pseudo-Smarandache function has a simple definition: Given any integer n > 0, the value of the Pseudo-Smarandache function is the smallest integer m such that n evenly divides the sum 1 + 2 + 3 + ... + m. In this paper, several problems concerning this function will be presented and solved. Most will involve the standard number theory functions such as Euler's phi function and the sum of divisors function. [1]

The Pseudo-Smarandache function has a simple definition: Given any integer n > 0, the value of the Pseudo-Smarandache function is the smallest integer m such that n evenly divides the sum 1 + 2 + 3 + ... + m. In this paper, several problems concerning this function will be presented and solved. Most will involve the standard number theory functions such as Euler's phi function and the sum of divisors function. [1]

The Pseudo-Smarandache function has a simple definition: Given any integer n > 0, the value of the Pseudo-Smarandache function is the smallest integer m such that n evenly divides the sum 1 + 2 + 3 + ... + m. In this paper, several problems concerning this function will be presented and solved. Most will involve the standard number theory functions such as Euler's phi function and the sum of divisors function. [1]

"Number Theory: 215-217" is an article from The American Mathematical Monthly, Volume 21 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2972184

In this paper, we analyze some equations linked to the meaning of DN Constant. We describe new possible mathematical connections with the Ramanujan Recurring Numbers and some parameters of Number Theory, Theoretical Cosmology and String Theory

In this paper, we analyze some equations linked to the meaning of DN Constant. We describe new possible mathematical connections with the Ramanujan Recurring Numbers and some parameters of Number Theory, Theoretical Cosmology and String Theory

In this paper, we analyze some equations linked to the meaning of DN Constant. We describe new possible mathematical connections with the Ramanujan Recurring Numbers and some parameters of Number Theory, Theoretical Cosmology and String Theory

In [9], [15] it has been introduced a technique, based on nonstandard analysis, to study some problems in combinatorial number theory. In this paper we present three applications of this technique: the first one is a new proof of a known result regarding the algebra of \betaN, namely that the center of the semigroup (\beta\mathbb{N};\oplus) is \mathbb{N}; the second one is a generalization of a theorem of Bergelson and Hindman on arithmetic progressions of lenght three; the third one regards the partition regular polynomials in Z[X], namely the polynomials in Z[X] that have a monochromatic solution for every finite coloration of N. We will study this last application in more detail: we will prove some algebraical properties of the sets of such polynomials and we will present a few examples of nonlinear partition regular polynomials. In the first part of the paper we will recall the main results of the nonstandard technique that we want to use, which is based on a characterization of ultrafilters by means of nonstandard analysis.

This unit begins the second part of the course, in which we will investigate a class of methods in analytic number theory known as sieves. (For non-native speakers of English: in ordinary life, a sieve is a device through which you pour a powder, like �our, to �lter out large impurities.) Whereas the �rst part of the course leaned heavily on methods from complex analysis, here the emphasis will be more combinatorial.

This unit begins the second part of the course, in which we will investigate a class of methods in analytic number theory known as sieves. (For non-native speakers of English: in ordinary life, a sieve is a device through which you pour a powder, like �our, to �lter out large impurities.) Whereas the �rst part of the course leaned heavily on methods from complex analysis, here the emphasis will be more combinatorial.

"Number Theory and Diophantine Analysis: 187-189" is an article from The American Mathematical Monthly, Volume 20 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2974091

"Number Theory and Diophantine Analysis: 187-189" is an article from The American Mathematical Monthly, Volume 20 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2974091

"Number Theory and Diophantine Analysis: 187-189" is an article from The American Mathematical Monthly, Volume 20 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2974091

"Number Theory and Diophantine Analysis: 187-189" is an article from The American Mathematical Monthly, Volume 20 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2974091

Elementary Number Theory, Underwood Dudley, Dover publications, 2nd edition, 2008.

In this unit, we prove the Bombieri-Vinogradov theorem, in the form stated in the previous unit.

In this unit, we prove the Bombieri-Vinogradov theorem, in the form stated in the previous unit.

Motivated by the similarity between cubic string field theory (CSFT) and the Chern-Simons theory in three dimensions, we study the possibility of interpreting N=(\pi^2/3)\int(U Q_B U^{-1})^3 as a kind of winding number in CSFT taking quantized values. In particular, we focus on the expression of N as the integration of a BRST-exact quantity, N=\int Q_B A, which vanishes identically in naive treatments. For realizing non-trivial N, we need a regularization for divergences from the zero eigenvalue of the operator K in the KBc algebra. This regularization must at same time violate the BRST-exactness of the integrand of N. By adopting the regularization of shifting K by a positive infinitesimal, we obtain the desired value N[(U_tv)^{\pm 1}]=\mp 1 for U_tv corresponding to the tachyon vacuum. However, we find that N[(U_tv)^{\pm 2}] differs from \mp 2, the value expected from the additive law of N. This result may be understood from the fact that \Psi=U Q_B U^{-1} with U=(U_tv)^{\pm 2} does not satisfy the CSFT EOM in the strong sense and hence is not truly a pure-gauge in our regularization.

In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Z_p-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi and Perrin-Riou, we define restricted Selmer groups and \lambda^\pm, \mu^\pm-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms of these invariants. To be able to work with non-cyclotomic Z_p-extensions, a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified Z_p-extension of Q_p.

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.

According to Wilson's theory of critical phenomena, critical exponents are universal functions of $d$, the dimension of space, and $n$, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where $T_N$ and $T_c$ intersect. By measuring critical exponents close to the bicritical point, and knowing that $d=3$, one can experimentally measure the number 5 of the SO(5) theory.

According to Wilson's theory of critical phenomena, critical exponents are universal functions of $d$, the dimension of space, and $n$, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where $T_N$ and $T_c$ intersect. By measuring critical exponents close to the bicritical point, and knowing that $d=3$, one can experimentally measure the number 5 of the SO(5) theory.

According to Wilson's theory of critical phenomena, critical exponents are universal functions of $d$, the dimension of space, and $n$, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where $T_N$ and $T_c$ intersect. By measuring critical exponents close to the bicritical point, and knowing that $d=3$, one can experimentally measure the number 5 of the SO(5) theory.

According to Wilson's theory of critical phenomena, critical exponents are universal functions of $d$, the dimension of space, and $n$, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where $T_N$ and $T_c$ intersect. By measuring critical exponents close to the bicritical point, and knowing that $d=3$, one can experimentally measure the number 5 of the SO(5) theory.

On the Theory of Correlation for any Number of Variables, Treated by a New System of Notation. Yule, G. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character (1905-1934). 1907-05-14. 79 (529):182–193