For infinitely many primes p = 4k+1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Zp such that the difference set B−B contains only quadratic residues. Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B| ≤ √ p − 1, under suitable conditions on p. The new bound is valid for approximately three quarters of the primes p = 4k + 1.

AND A BOUND FOR THE FIRST FACTOR OF THE CLASS NUMBER1 L. CARLITZ 1. Let p be a prime e¿3. For (r, p) = l define r' by means of rr' = l(mod£); also let R(r) denote the least positive residue of r (mod p). Maillet defined the determinant Dp of order (p—1)/2 by means of (1) A, R(rs') | (r, s = 1, • • • , (p l)/2) and raised the question whether Dp^0 for all p. Malo computed Dp for p^ 13 and conjec...

introduction integrated nutrient management involving crop residue/green manures and chemical fertilizer is potential alternative to provide a balanced supply of nutrients, enhance soil quality and thereby sustain higher productivity. the present experiment was undertaken to evaluate the effect of different crop residue management practices and npk levels on yield components and yield of wheat....

The Residue Number System (RNS) is a non-weighted system that is very efficient in digital signal processing and communicational applications. The previous proposed methods for the residue to binary (R/B) conversions are based on the Chinese Reminder Theorem (CRT) or Mixed Radix Conversion (MRC). These theorems are difficult to implement. In this paper, we present a new highspeed ROM-less resid...

The ability of a watershed model to mimic specified watershed processes is assessed through the calibration and validation process. The Soil and Water Assessment Tool (SWAT) watershed model was implemented in the Beaver Reservoir Watershed of Northwest Arkansas. The objectives were to: (1) provide detailed information on calibrating and applying a multisite and multivariable SWAT model; (2) con...

It is shown that every dp-minimal integral domain R a local ring and for non-maximal prime ideal ℘ of R, the localization R℘ valuation ℘R℘ = ℘. Furthermore, if only its residue field infinite or finite maximal principal.

mulches often use for weed control, hold soil moisture, decrease soil temperature, soil fertility, soil conservation, soil against rain and soil quality in organic farming. a field experiment was conducted to evaluate the effect of different wheat residue and sunflower densities on sunflower growth and yield during 2007 growing season at the research field of birjand university. the experimenta...

crop residue is a non-chemical method of weed control in agricultural sustainable systems. this research was conducted at the alarogh site of ardabilto evaluate the effect of integrated use of mulch and herbicide on weed emergence and growth in potato in 2007. treatments were four levels herbicide including: (1) paraquat [n,n'-dimethyl-4,4'-bipyridinium dichloride] herbicide as pre-pl...