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.

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.

MULTIPLICATION OPERATORS ON WEIGHTED DIRICHLET SPACES

In this paper,we study multiplication operators on weighted Dirichlet spaces D_(β)(β∈R).Let n be a positive integer and β∈R,we show that the multiplication operator M_(z)^(n) on D_(β) is similar to the operator ⊕_(1)^(n)M_(z)on the space⊕_(1)^(n)D_(β).Moreover,we prove that M_(z)^(n)(≥2)on Dβis unitarily equivalent to ⊕_(1)^(n)M_(z) on⊕_(1)^(n)D_(β) if and only if β=0.In addition,we completely characterize the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces z^(k)D_(β)(k≥1),and the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces S_(j)(0≤j<n).Abkar,Cao and Zhu[Complex Anal Oper Theory,2020,14:Art 58]pointed out that it is an important,natural,and difficult question in operator theory to identify the commutant of a bounded linear operator.They characterized the commutant A′( M_(z)^(n))of M_(z)^(n)on a family of analytic function spaces A_(α)^(2)(α∈R)on D(in fact,the family of spaces A_(α)^(2)(α∈R)is the same with the family of spaces D_(β)(β∈R))in terms of the multiplier algebra of the underlying function spaces.In this paper,we give a new characterization of the commutant A′( M_(z)^(n))of M_(z)^(n)on D_(β),and characterize the self-adjoint operators and unitary operators in A'(M_(z)^(n)).We find that the class of self-adjoint operators(unitary operators)in A'(M_(z)^(n))when β≠0 is different from the class of self-adjoint operators(unitary operators)in A′( M_(z)^(n))when β=0.

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.

Infiltration by monocytes of the central nervous system and its role in multiple sclerosis: reflections on therapeutic strategies

Mononuclear macrophage infiltration in the central nervous system is a prominent feature of neuroinflammation. Recent studies on the pathogenesis and progression of multiple sclerosis have highlighted the multiple roles of mononuclear macrophages in the neuroinflammatory process. Monocytes play a significant role in neuroinflammation, and managing neuroinflammation by manipulating peripheral monocytes stands out as an effective strategy for the treatment of multiple sclerosis, leading to improved patient outcomes. This review outlines the steps involved in the entry of myeloid monocytes into the central nervous system that are targets for effective intervention: the activation of bone marrow hematopoiesis, migration of monocytes in the blood, and penetration of the blood–brain barrier by monocytes. Finally, we summarize the different monocyte subpopulations and their effects on the central nervous system based on phenotypic differences. As activated microglia resemble monocyte-derived macrophages, it is important to accurately identify the role of monocyte-derived macrophages in disease. Depending on the roles played by monocyte-derived macrophages at different stages of the disease, several of these processes can be interrupted to limit neuroinflammation and improve patient prognosis. Here, we discuss possible strategies to target monocytes in neurological diseases, focusing on three key aspects of monocyte infiltration into the central nervous system, to provide new ideas for the treatment of neurodegenerative diseases.

Multiple endocrine neoplasia type 1:Early diagnosis is very important

In this manuscript,we comment on a recent publication by Yuan et al.This article provides a detailed scientific diagnostic process for a multiple endocrine neo-plasia type 1 patient,thus offering strong guidance for clinical practice.However,we believe that the authors should also provide information on the patient's long-term prognosis.

Pegaspargase induced multiple organ failure with acute lymphoblastic leukemia:A case report

BACKGROUND The introduction of pegaspargase has greatly advanced the treatment of acute lymphoblastic leukemia(ALL).In the literature,only one case of pegaspargaseinduced multiple organ failure has been reported,and the patient died due to multiple organ failure.CASE SUMMARY Herein,we present a rare case of a 40-year-old man with ALL who developed multiple organ failure after treatment with pegaspargase.The patient had two rare phenomena reflecting poor prognosis,including the discrepancy between clinical manifestations and liver function and persistently low alpha-fetoprotein(AFP)levels from subacute liver failure.However,the patient was successfully treated using a multidisciplinary team approach.CONCLUSION This is the first case report of successful treatment of pegaspargase-induced multiple organ failure.The findings emphasize the importance of a multidisciplinary team approach in treating pegaspargase-induced multiple organ failure.

Optimizing distribution of multiple tuned mass dampers for building structures with inverse element exchange method

Multiple tuned mass dampers(MTMDs)reduce dynamic response with multiple specified frequencies of building structures.Many optimization algorithms for placement design exist,though they rarely conform to code-based verification nor produce high quality solutions without high computational effort and high complexity.This study proposes an inverse element exchange method(IEEM)with multi-level programming and compares it to a single tuned mass damper(STMD)and uniform distribution of multiple tuned mass dampers in the frequency and time domains.A ten-story shear building is used for the numerical case study.The results show that the proposed method can offer improvement over the STMD,uniform distribution of multiple tuned mass dampers,and distribution optimized by genetic algorithms(GA)with regard to minimizing the interstory drift ratio(IDR)in both the frequency and time domains and the time consumption for optimization.

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.

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.

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 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%.

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.

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.

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 ■.

ON MULTIPLICATION AND COMULTIPLICATION MODULES

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

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.

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.

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,...,＋∞}.