Leon Bernstein
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View article: Periodic Algorithms and their Application
Periodic Algorithms and their Application Open
In two previous papers [ 1 , 2 ] we investigated the zeros of certain arithmetic functions. Using units of cubic fields, we also succeeded to construct, almost by accident, and as a by-product so to speak, entirely new and comparatively co…
View article: Gaining Units from Units
Gaining Units from Units Open
Dirichlet was the first to give an ingenious proof of the exact (finite) number of elements in the basis of the multiplicative group of units in any algebraic number field of arbitrary degree n. These elements are called fundamental units.…
View article: Fundamental units and cycles in the period of real quadratic number fields. I
Fundamental units and cycles in the period of real quadratic number fields. I Open
PART I 0. Introduction.In this paper we introduce the concept of "Cycles in the Period" of the simple continued fraction expansion of a real quadratic irrational.This is expressed in the DEFINITION.Let M, D, d be positive rational integers…
View article: Units and periodic Jacobi-Perron algorithms in real algebraic number fields of degree $3$
Units and periodic Jacobi-Perron algorithms in real algebraic number fields of degree $3$ Open
It is not known whether or not the Jacobi-Perron Algorithm of a vector in ${R_{n - 1}},n \geqslant 3$, whose components are algebraic irrationals, always becomes periodic. The author enumerates, from his previous papers, a few infinite cla…
View article: On the Diophantine Equation <i>x</i>(<i>x + d</i>)(<i>x + 2d</i>) +<i>y</i>(<i>y + d</i>)(<i>y + 2d</i>) = <i>z</i>(<i>z + d</i>)(<i>z + 2d</i>)
On the Diophantine Equation <i>x</i>(<i>x + d</i>)(<i>x + 2d</i>) +<i>y</i>(<i>y + d</i>)(<i>y + 2d</i>) = <i>z</i>(<i>z + d</i>)(<i>z + 2d</i>) Open
A previous result of the author concerning the parametric representation of infinitely many solutions of the title equation is strongly improved. New classes each containing infinitely many solutions of the equation for specified values of…
View article: The Jacobi-Perron algorithm and the algebra of recursive sequences
The Jacobi-Perron algorithm and the algebra of recursive sequences Open
This paper shows the existence of a one-to-one correspondence between a certain class of square matrices of arbitrary order and a related extension field. The elements of these matrices are obtained from certain basic linear recursive sequ…
View article: Salt Tolerance of Ornamental Shrubs and Ground Covers1
Salt Tolerance of Ornamental Shrubs and Ground Covers1 Open
The salt tolerance of 25 shrub and ground-cover species was determined in plots artificially salinized with NaCl + CaCl 2 . Chloride and Na injury was observed in sand cultures of the same species with 4 different salt treatments. Tolerant…
View article: Explicit Solutions of Pyramidal Diophantine Equations
Explicit Solutions of Pyramidal Diophantine Equations Open
Let P m, k denote the set of pyramidal numbers 1.1 The question has been asked whether there exist elements p , q , r in P m, k such that p + q = r or, as the problem is usually posed, 1.2 The case k =2 has been studied by Sierpinski [6] a…
View article: Method for Determining Solutes in the Cell Walls of Leaves
Method for Determining Solutes in the Cell Walls of Leaves Open
A perfusion method is described whereby large discs of amphistomatous leaves are vacuum-perfused with water so that either successive fractions of perfusate may be analyzed for solutes or the infused water may be displaced and collected af…
View article: Effect of Grape Rootstocks on Chloride Accumulation in Leaves1
Effect of Grape Rootstocks on Chloride Accumulation in Leaves1 Open
The effect of 5 rootstocks on chloride accumulation in ‘Cardinal’ and ‘Thompson Seedless’ scions was studied for 3 years in large sand cultures containing 12.5, 25, and 50 meq Cl - /liter of culture solution. Rootstock effects were unprece…
View article: New infinite classes of periodic Jacobi-Perron algorithms
New infinite classes of periodic Jacobi-Perron algorithms Open
The question whether a system of n -1 real algebraic numbers (n = 2, 3, •) chosen from an algebraic field of degree not higher than n 9 yields periodicity by Jacobi's Algorithm is still as open and challenging as hundred years ago.The pres…
View article: A Periodic Jacobi-Perron Algorithm
A Periodic Jacobi-Perron Algorithm Open
In the first part of this paper I shall demonstrate that one irrational root of the algebraic equation creates an algebraic number field, out of which n — 1 irrationals can be chosen so that they yield a periodic Jacobi-Perron algorithm. T…
View article: Salt tolerance of safflower.
Salt tolerance of safflower. Open
Safflower is highly salt tolerant, according to results of field plot experiments in 1962 and 1963 However, safflower appears to be only about half as salt tolerant during germination as during later stages of growth Salinity decreases the…
View article: Salt Tolerance of Plants
Salt Tolerance of Plants Open
Crop Production/Industries
View article: Salt Tolerance of Vegetable Crops in the West
Salt Tolerance of Vegetable Crops in the West Open
Excerpt from the report: Soil salinity, or saltiness, is a widespread condition in arid and semiarid areas and along low-lying seacoasts. Wherever irrigation is practiced, excessive amounts of soluble salts in the irrigation water or soil …
View article: THE INFLUENCE OF MINERAL NUTRITION, SOIL FERTILITY, AND CLIMATE ON CAROTENE AND ASCORBIC ACID CONTENT OF TURNIP GREENS
THE INFLUENCE OF MINERAL NUTRITION, SOIL FERTILITY, AND CLIMATE ON CAROTENE AND ASCORBIC ACID CONTENT OF TURNIP GREENS Open
Previous investigations from this laboratory with tomatoes (2, 7) have indicated that the ascorbic acid and carotene content of the tomato fruit is influenced but little by the supply of mineral nutrients to the plants.This work was done w…