A Judgment of Integer Coefficient Polynomials without Integer Root

2019 ◽  
Vol 09 (06) ◽  
pp. 699-701
Author(s):  
棉棉 张
Keyword(s):  
Integer Coefficient

scholarly journals Beyond non-integer Hill coefficients: A novel approach to analyzing binding data, applied to Na+-driven transporters

2015 ◽  
Vol 145 (6) ◽  
pp. 555-563 ◽  
Author(s):  
Silvia Ravera ◽  
Matthias Quick ◽  
Juan P. Nicola ◽  
Nancy Carrasco ◽  
L. Mario Amzel
Keyword(s):  
Hill Equation ◽  
Integer Coefficient ◽  
Novel Approach ◽  
Binding Data ◽  
Na Ions ◽  
Hill Coefficients ◽  
Integer Exponent ◽  
The Individual ◽  
The Hill ◽  
Analyze Data

Prokaryotic and eukaryotic Na+-driven transporters couple the movement of one or more Na+ ions down their electrochemical gradient to the active transport of a variety of solutes. When more than one Na+ is involved, Na+-binding data are usually analyzed using the Hill equation with a non-integer exponent n. The results of this analysis are an overall Kd-like constant equal to the concentration of ligand that produces half saturation and n, a measure of cooperativity. This information is usually insufficient to provide the basis for mechanistic models. In the case of transport using two Na+ ions, an n < 2 indicates that molecules with only one of the two sites occupied are present at low saturation. Here, we propose a new way of analyzing Na+-binding data for the case of two Na+ ions that, by taking into account binding to individual sites, provides far more information than can be obtained by using the Hill equation with a non-integer coefficient: it yields pairs of possible values for the Na+ affinities of the individual sites that can only vary within narrowly bounded ranges. To illustrate the advantages of the method, we present experimental scintillation proximity assay (SPA) data on binding of Na+ to the Na+/I− symporter (NIS). SPA is a method widely used to study the binding of Na+ to Na+-driven transporters. NIS is the key plasma membrane protein that mediates active I− transport in the thyroid gland, the first step in the biosynthesis of the thyroid hormones, of which iodine is an essential constituent. NIS activity is electrogenic, with a 2:1 Na+/I− transport stoichiometry. The formalism proposed here is general and can be used to analyze data on other proteins with two binding sites for the same substrate.

scholarly journals IMAGE RESOLUTION ENHANCEMENT OF SATELLITE IMAGES USING DYADIC INTEGER COEFFICIENT WAVELET FILTER FOR WAVELET TRANSFORM

2021 ◽  
Vol 9 (1) ◽  
pp. 971-975
Author(s):  
P.B. Chopade, P. N. Kota
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Satellite Images ◽  
Resolution Enhancement ◽  
Image Resolution ◽  
Integer Coefficient ◽  
Discrete Wavelet ◽  
Wavelet Filter ◽  
Hardware Complexity ◽  
Integer Coefficients

In this paper, image resolution enhancements for satellite images are proposed using dyadic integer coefficients based wavelet filter (DICWF). We proposes a technique in which discrete wavelet transform and stationary wavelet transform using DICWF which is used to obtain a high resolution image and this image is derived from frequency subbands. The satellite images play a very vital role now days in the development of technical aspects which needs to be enhanced. These satellite images are superresolved with the help of dyadic integer coefficient-based wavelet filters, which reduces the hardware complexity and computational difficulties due to the rational and integer coefficients of these filter banks. The value of the peak signal-to-noise ratio (PSNR) of the proposed method and the resultant visual images of the proposed method show the effectiveness of this algorithm over other existing algorithms using discrete wavelet transform. Noise can be minimized by applying thresholding on different frequency subbands which obtained by the application of DICWF to the noisy, blurred input images.

scholarly journals Divide and Conquer: Towards Faster Pseudo-Boolean Solving

2018 ◽  
Author(s):  
Jan Elffers ◽  
Jakob Nordström
Keyword(s):  
Boolean Satisfiability ◽  
Conflict Analysis ◽  
Divide And Conquer ◽  
Theoretical Strength ◽  
Integer Coefficient ◽  
Sat Solvers ◽  
Wide Range ◽  
Clause Learning

The last 20 years have seen dramatic improvements in the performance of algorithms for Boolean satisfiability---so-called SAT solvers---and today conflict-driven clause learning (CDCL) solvers are routinely used in a wide range of application areas. One serious short-coming of CDCL, however, is that the underlying method of reasoning is quite weak. A tantalizing solution is to instead use stronger pseudo-Boolean (PB) reasoning, but so far the promise of exponential gains in performance has failed to materialize---the increased theoretical strength seems hard to harness algorithmically, and in many applications CDCL-based methods are still superior. We propose a modified approach to pseudo-Boolean solving based on division instead of the saturation rule used in [Chai and Kuehlmann '05] and other PB solvers. In addition to resulting in a stronger conflict analysis, this also improves performance by keeping integer coefficient sizes down, and yields a very competitive solver as shown by the results in the Pseudo-Boolean Competitions 2015 and 2016.

scholarly journals Special Dio 3 - Tuples

2014 ◽  
Vol 10 ◽  
pp. 22-25
Author(s):  
M.A. Gopalan ◽  
K. Geetha ◽  
Manju Somanath
Keyword(s):  
Integer Coefficient

We search for three distinct polynomials with integer coefficient such that the product of anytwo members of the set minus their sum and increased by a non-zero integer (or polynomial withinteger coefficient) is a perfect square.

scholarly journals Image Watermarking Based on IWT and Parity Bit Checking

2021 ◽  
pp. 2726-2739
Author(s):  
Jalal H. Awad ◽  
Balsam D. Majeed
Keyword(s):  
Wavelet Transform ◽  
Image Quality ◽  
Signal To Noise Ratio ◽  
Image Watermarking ◽  
Similarity Index ◽  
Structural Similarity ◽  
Floating Point ◽  
Integer Coefficient ◽  
Authentication Mechanism ◽  
Image Pixels

     Various document types play an influential role in a lot of our lives activities today; hence preserving their integrity is an important matter. Such documents have various forms, including texts, videos, sounds, and images.  The latter types' authentication will be our concern here in this paper. Images can be handled spatially by doing the proper modification directly on their pixel values or spectrally through conducting some adjustments to some of the addressed coefficients. Due to spectral (frequency) domain flexibility in handling data, the domain coefficients are utilized for the watermark embedding purpose. The integer wavelet transform (IWT), which is a wavelet transform based on the lifting scheme, is adopted in this paper in order to provide a direct way for converting image pixels' integer values to integer coefficient values rather than floating point coefficients that could be produced by the traditional wavelet transform. This direct relation can enhance the processed image quality due to avoiding the rounding operations on the floating point coefficients. The well-known parity bit approach is also utilized in this paper as an authentication mechanism, where 3 secret parity bits are used for each block in an image which is divided into non-overlapped blocks in order to enforce a form of fragile watermark approach. Thus, any alteration in the block pixels could cause the adopted (even) parity to be violated. The fragile watermarking is achieved through the modification of least significant bits ((LSBs) of certain frequency coefficients' according to the even parity condition. In spite of this image watermarking operation, the proposed method is efficient. In order to prove the efficiency of our proposed method, it was tested against standard images using measurements like peak signal to noise ratio (PSNR) and structural similarity index (SSIM).  Experiments showed promising results; the method preserves high image quality (PSNR≈ 44.4367dB, SSIM≈ 0.9956) and good tamper detection capability.

scholarly journals Special Diophantine Triples Involving Square Pyramidal Numbers

2021 ◽  
Vol 1 (2) ◽  
pp. 27-29
Author(s):  
Saranya C. ◽  
Achya B.
Keyword(s):  
Integer Coefficient ◽  
Diophantine Triples

In this communication, we accomplish special Diophantine triples comprising of square pyramidal numbers such that the product of any two members of the set added by their sum and increased by a polynomial with integer coefficient is a perfect square.

Sign in / Sign up

Export Citation Format

Share Document