Improving Video Watermarking through Galois Field GF(2^(4)) Multiplication Tables with Diverse Irreducible Polynomials and Adaptive Techniques

Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity.This study delves into the integration of Galois Field(GF)multiplication tables,especially GF(2^(4)),and their interaction with distinct irreducible polynomials.The primary aim is to enhance watermarking techniques for achieving imperceptibility,robustness,and efficient execution time.The research employs scene selection and adaptive thresholding techniques to streamline the watermarking process.Scene selection is used strategically to embed watermarks in the most vital frames of the video,while adaptive thresholding methods ensure that the watermarking process adheres to imperceptibility criteria,maintaining the video's visual quality.Concurrently,careful consideration is given to execution time,crucial in real-world scenarios,to balance efficiency and efficacy.The Peak Signal-to-Noise Ratio(PSNR)serves as a pivotal metric to gauge the watermark's imperceptibility and video quality.The study explores various irreducible polynomials,navigating the trade-offs between computational efficiency and watermark imperceptibility.In parallel,the study pays careful attention to the execution time,a paramount consideration in real-world scenarios,to strike a balance between efficiency and efficacy.This comprehensive analysis provides valuable insights into the interplay of GF multiplication tables,diverse irreducible polynomials,scene selection,adaptive thresholding,imperceptibility,and execution time.The evaluation of the proposed algorithm's robustness was conducted using PSNR and NC metrics,and it was subjected to assessment under the impact of five distinct attack scenarios.These findings contribute to the development of watermarking strategies that balance imperceptibility,robustness,and processing efficiency,enhancing the field's practicality and effectiveness.

The Cumulative Method for Multiplication and Division

This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.

Mode Multiplication of Cylindrical Vector Beam Using Raytracing Control

Cylindrical vector beams(CVBs)hold significant promise in mode division multiplexing communication owing to their inherent vector mode orthogonality.However,existing studies for facilitating CVB channel processing are confined to mode shift conversions due to their reliance on spin-dependent helical modulations,overlooking the pursuit of mode multiplication conversion.This challenge lies in the multiplicative operation upon inhomogeneous vector mode manipulation,which is expected to advance versatile CVB channel switching and routing.Here,we tackle this gap by introducing a raytracing control strategy that conformally maps the light rays of CVB from the whole annulus distribution to an annular sector counterpart.Incorporated with the multifold conformal annulus-sector mappings and polarization-insensitive phase modulations,this approach facilitates the parallel transformation of input CVB into multiple complementary components,enabling the mode multiplication conversion with protected vector structure.Serving as a demonstration,we experimentally implemented the multiplicative operation of four CVB modes with the multiplier factors of N=+2 and N=−3,achieving the converted mode purities over 94.24%and 88.37%.Subsequently,200 Gbit/s quadrature phase shift keying signals were successfully transmitted upon multiplicative switching of four CVB channels,with the bit-error-rate approaching 1×10^(−6).These results underscore our strategy’s efficacy in CVB mode multiplication,which may open promising prospects for its advanced applications.

A quantum algorithm for Toeplitz matrix-vector multiplication

Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.

Effects of Exogenous Hormones on Subculture Multiplication and Root Induction of Tissuecultured Seedlings of Mulberry

Objective The purpose of this experiment was to investigate the effects of exogenous hormone factors on subculture multiplication and root induction of tis-suecultured seedlings in mulberry. [Method] The aseptic seedlings of Guisangyou 12 were used as the materials and the comparative experiment on subculture multi-plication and root induction used different kinds,concentrations and combinations of exogenous hormones. [Result] The hormone combination of 0.1 mg/L IBA＋1.5 mg/L 6-BA＋0.03 mg/L TDZ showed the best effects to bud multiplication, and the multiple of bud multiplication was 5.28. The effects of NAA was better than IBA and IAA on root induction. The hormone combination of 2.0 mg/L NAA＋1.0 mg/L PP333 was most suitable to the root induction, in which the rooting rate arrived to 100%, the root number was 7.01 and the root length was 1.38 cm on average. [Conclusion] The results wil provide some technical reference for large-scale propagation of mul-berry seedlings in vitro.

ON MULTIPLICATION AND COMULTIPLICATION MODULES

This article deals with some results concerning multiplication and comultipli- cation modules over a commutative ring.

Research on a Method for Purification and Multiplication of PTGMS Lines

[Objective] The aims was to explore PTGMS line purification and multipli- cation technology. [Method] Three commercial PTGMS lines, Annong 810S, P88S and C815S, were used in this study. In the first year, two sterile line populations with same genetic background were multiplied by dividing seedling; meanwhile, se- lection and multiplication of the core individuals were conducted; within the year, the core seeds harvested were multiplied under the isolated condition in Hainan, and at the same time, superior individuals were selected and used as the seeds for two populations with same genetic background in the next year. In the second year, seeds harvested in Hainan were planted in Changsha, while the core individuals were selected and multiplied; the core seeds harvested were continued to multiply in Hainan. The above procedures were repeated in the following years. [Result] The test results showed that in two years the proportion of core individuals in the popu- lation of Annong 810S, P88S and C815S increased from 40.3%, 0.7% and 0.3% in the first year to 71.67%, 66.00% and 68.67% in the second year respectively. [Conclusion] This suggested that this method of purification and multiplication of the PTGMS lines for consecutive years can effectively control the drift of the critical sterility inducing temperature, and at the same time, core seeds with high purity and controlled inducing temperature can be harvested.

Study on Designing Standards System Framework of Hainan National Breeding and Multiplication

A preliminary feasibility study was set up for the HNBM standard system. By introducing the set theory and basic methods of the solid geometry and adopting the Verman three-dimensional structure ideology innovatively, the standards system of Hainan National Breeding and Multiplication (HNBM) was studied with the four-dimensional structure and integration by combining with the time dimension. The four-dimensional structure standards system will be useful for guiding the construction of the HNBM standards system, carrying on the division of labor and realizing the dynamic development of the standards system. The standards set of HNBM helps to computer programming and information management.

Study on Multiplication, Rooting and Transplanting of Tissue Culture Plantlets of Rhododendron chrysanthum Pall

[Objective] This study aimed to shorten the multiplication culture and root- ing culture periods of Rh. chrysanthum Pall. [Method] The Rh. chrysanthum Pall tis- sue culture plantlets collected from Changbai Mountain were used as material, and the effects of different hormone combinations and coconut milk on the proliferation and differentiation of Rh. chrysanthum Pall tissue culture plantlets were investigated. In addition, the rooting medium and transplanting matrix for Rh. chrysanthum Pall tissue culture plantlets were explored. [Result] The medium composed of modified MS, iBA （3 mg/L） and ZT （1.5 mg/L） was the optimum medium for subculture mul- tiplication of Rh. chrysanthum Pall tissue culture plantlets. The multiplication multiple and average plant height were significantly improved by adding coconut milk into the medium （150 mg/L）. [Conclusion] For Rh. chrysanthum Pall tissue culture plantlets, the optimum rooting culture medium was composed of modified MS （1/4） and IBA （5.0 mg/L）, and the tissue culture plantlets began to root 8 d after the inoculation. The root induction treatment was carried out after a 15-d sand culture, and the suitable matrix was composed of tufty soil, humus soil and perlite （2：1：1） with a survival rate of 95.66%.

Analysis of the Key Issues about the Regularized Construction of Hainan National Breeding and Multiplication Base

Based on winter nursery and shuttle breeding, Hainan National Breeding and Multiplication （HNBM）, with off-season breeding and seed production as the essence, has become a national strategic resource. The way of HNBM rising to the national strategy was analyzed through the aspects of technology features, historical characteristics, irreplaceability, function and value hierarchy, and the key problems. As the major achievement of the practice of scientific research and historical selec- tion, HNBM played an irreplaceable role in the climatic conditions, scientific breed- ing, and seed production in disaster relief, protecting the safety of the seed industry and Iocational advantages. Based on the analysis on the functions, values and ex- isted problems of HNBM, the function and value hierarchical structure of HNBM was established through introducing concepts of value engineering, industrial clusters and regional economy. But to fully achieve the industrial clustering development and functional values of HNBM, it needed to solve the key problems existed in top-level planning, experimental bases, system design, hardware construction and ecological security. Some suggestions were put forward in this paper, including setting up key scientific research protection zones, improving the regulations and policies safeguard mechanism and management system of HNBM, drawing up and carrying out the base development planning of HNBM, and striving for financial support from national policies.

Fast and secure elliptic curve scalar multiplication algorithm based on special addition chains

To resist the side chaimel attacks of elliptic curve cryptography, a new fast and secure point multiplication algorithm is proposed. The algorithm is based on a particular kind of addition chains involving only additions, providing a natural protection against side channel attacks. Moreover, the new addition formulae that take into account the specific structure of those chains making point multiplication very efficient are proposed. The point multiplication algorithm only needs 1 719 multiplications for the SAC260 of 160-bit integers. For chains of length from 280 to 260, the proposed method outperforms all the previous methods with a gain of 26% to 31% over double-and add, 16% to22% over NAF, 7% to 13% over4-NAF and 1% to 8% over the present best algorithm--double-base chain.

Multiplication Model of EMCCD Based on Single Type of Carrier

The avalanche multiplication principle of electron multiplication CCD (EMCCD) was discussed on the basis of single type of carrier, and the multiplication model was built by using a classic piecewise ionization rate model and avalanche multiplication integral formula. Wolff's ionization rate model was selected according to the structure and the multiplication gate amplitude of the actual devices. Compared the theoretical result with the multiplication curve of the actual device, it was found that only enough fringing field strength and multiplication area length could lead to adequate signal charge multiplication. The relationship between the multiplication gate amplitude and the total gain of the cascaded boosting EMCCD can be conveniently determined by using this model.

A SCALABLE HYBRID MODULAR MULTIPLICATION ALGORITHM

Based on the analysis of several familiar large integer modular multiplication algorithms, this paper proposes a new Scalable Hybrid modular multiplication (SHyb) algorithm which has scalable operands, and presents an RSA algorithm model with scalable key size. Theoretical analysis shows that SHyb algorithm requires m 2 n /2 + 2miterations to complete an mn-bit modular multiplication with the application of an n-bit modular addition hardware circuit. The number of the required iterations can be reduced to a half of that of the scalable Montgomery algorithm. Consequently, the application scope of the RSA cryptosystem is expanded and its operation speed is enhanced based on SHyb al- gorithm.

POINTWISE MULTIPLICATION OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF ■

This article is devoted to characterizing the boundedness and compactness of multiplication operators from Hardy spaces to weighted Bergman spaces in the unit ball of ■.

Studies on Rhizome Multiplication and Differentiation of Cymbidium sinense × Cymbidium goeringii

With the rhizomes obtained from the germination of Cymbidium sinense ~ Cymbidium goeringii seeds as a material, the effects of different basic media and different plant growth regulators on the multiplication and differentiation of rhizomes and rooting and transplanting of seedlings were investigated. The results showed that the basal medium more suitable for the multiplication and differentiation of rhizomes was 1/2MS; the medium more suitable for the multiplication and differentiation of rhizomes of the hybrid orchid was 1/2MS ＋ 6 - BA 2.0 mg/L ＋ KT 0.5 mg/L ＋ NAA 0.05 mg/L; the medium more suitable for the rooting of the hybrid orchid was 1/2MS ＋ IBA 0.5 mg/L; and after training of seedlings, transplanting was performed onto moss, and after 25 d, the survival rate was 95.6%.

Shoot multiplication of Syringa reticulata var.mandshurica from in vitro cultured seedlings

We developed a shoot multiplication protocol for Syringa reticulata Blume vat. mandshurica Hara from in vitro cultured seedlings that derived from in vitro germinated seeds. The shoots could be induced on Murashige and Skoog （MS） medium with proper plant growth regulator combinations of 6-benzylaminopurine （BA） and indole-3-butyric acid （IBA）. The better medium for shoot multiplication and growth was MS ＋ 5 mg L-1 BA ＋ 0.5 mg L-1 IBA ＋ 20 g L-1 sucrose ＋ 7 g L-1 agar, and the corresponding shoot induction rate was 75 %. The plantlets grew well after rooting on I/2MS medium （macro-elements of MS medium are at half-strength） sup- plemented with 1 mg L-1 IBA, and the survival percentage was 〉80 % at 16 weeks after transplanting.

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

A rapid multiplication system for'Candidatus Liberibacter asiaticus'through regeneration of axillary buds in vitro

‘Candidatus Liberibacter asiaticus(CLas)’,which causes citrus Huanglongbing(HLB)disease,has not been successfully cultured in vitro to date.Here,a rapid multiplication system for CLas was established through in vitro regeneration of axillary buds from CLas-infected‘Changyecheng’sweet orange(Citrus sinensis Osbeck).Stem segments with a single axillary bud were cultured in vitro to allow CLas to multiply in the regenerating axillary buds.A high CLas titer was detected in the regenerated shoots on an optimized medium at 30 days after germination(DAG).This titer was 28.2-fold higher than in the midribs from CLas-infected trees growing in the greenhouse.To minimize contamination during in vitro regeneration,CLas-infected axillary buds were micrografted onto seedlings of‘Changyecheng’sweet orange and cultured in a liquid medium.In this culture,the titers of CLas in regenerated shoots rapidly increased from 7.5×10^(4)to 1.4×10^(8)cellsμg^(-1)of citrus DNA during the first 40 DAG.The percentages of shoots with>1×10^(8)CLas cellsμg^(-1)DNA were 30 and 40%at 30 and 40 DAG,respectively.Direct tissue blot immunoassay(DTBIA)indicated that the distribution of CLas was much more uniform in regenerated plantlets than in CLas-infected trees growing in the greenhouse.The disease symptoms in the plantlets were die-back,stunted growth,leaf necrosis/yellowing,and defoliation.The death rate of the plantlets was 82.0%at 60 DAG.Our results show that CLas can effectively multiply in citrus plantlests in vitro.This method will be useful for studying plant-HLB interactions and for rapid screening of therapeutic compounds against CLas in citrus.

Elliptic Curve Scalar Multiplication with x-Coordinate

This paper gives a comprehensive method to do Elliptic Curve Scalar Multiplication with only x-coordinate. Explicit point operation formulae for all types of defining equations of the curves are derived. For each type of curve, the performance is analyzed. The formulae are applied in Montgomery Ladder to get scalar multiplication algorithm operated with only x-coordinate. The new scalar multiplication has the same security level and computation amount with protected binary scalar multiplication （PBSM） against side channel attack, and has the advantages of higher security and little memory needed.

Code Design and Latency Analysis of Distributed Matrix Multiplication with Straggling Servers in Fading Channels

This paper exploits coding to speed up computation offloading in a multi-server mobile edge computing(MEC)network with straggling servers and channel fading.The specific task we consider is to compute the product between a user-generated input data matrix and a large-scale model matrix that is stored distributively across the multiple edge nodes.The key idea of coding is to introduce computation redundancy to improve robustness against straggling servers and to create communication redundancy to improve reliability against channel fading.We utilize the hybrid design of maximum distance separable(MDS)coding and repetition coding.Based on the hybrid coding scheme,we conduct theoretical analysis on the average task uploading time,average edge computing time,and average output downloading time,respectively and then obtain the end-to-end task execution time.Numerical results demonstrate that when the task uploading phase or the edge computing phase is the performance bottleneck,the hybrid coding reduces to MDS coding;when the downlink transmission is the bottleneck,the hybrid coding reduces to repetition coding.The hybrid coding also outperforms the entangled polynomial coding that causes higher uplink and downlink communication loads.