Search for Monic Irreducible Polynomials with Decimal Equivalents of Polynomials over Galois Field <I>GF</I>(<I>p^q</I>)

Substitution boxes or S-boxes play a significant role in encryption and de-cryption of bit level plaintext and cipher-text respectively. Irreducible Poly-nomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard, the ele-ments of 8-bit S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper, a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic Polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where?α∈ GF(pq)?and assume values from 2 to (p &#8722;1) to monic IPs.

Lag of accommodation predicts clinically significant change of spherical equivalents after cycloplegia

AIM: To evaluate related factors with the change of spherical equivalents(ΔSE) and determine the suitable predictor of clinically significant ΔSE(≥0.50 D) with cyclopentolate hydrochloride on Chinese children. METHODS: A total of 145 right eyes of 145 children aged 4 to 15 y were enrolled. Intraocular pressure, axial length and lag of accommodation(LOA) were assessed before cycloplegia induced by 3 drops of 1% cyclopentolate at 5-minute intervals. SE was measured before and 1 h after the first drop of cyclopentolate. ΔSE was compared between different gender groups and among refractive groups. Multivariate linear regression analysis was performed to find related factors with ΔSE. ROC analysis was used to figure out the suitable predictor of clinically significant ΔSE.RESULTS: For the total 145 eyes, the mean SE reached up to-0.70±1.86 D from-1.30±1.62 D, with the mean ΔSE of 0.60±0.55 D. The mean ΔSE were 0.63±0.55 D and 0.57±0.56 D respectively in the male and female group(P=0.40). The mean ΔSE was significantly different among different refractive groups(P<0.0001), with the ΔSE of hyperopia group(1.12±0.64 D) larger than that of the emmetropia(0.56±0.43 D, P=0.001) and myopia group(0.32±0.28 D, P<0.0001). The ΔSE was correlated with LOA(B=-0.54, P<0.0001), cycloplegic SE(B=0.10, P<0.0001) and age(B=-0.04, P=0.015). ROC curve indicated that LOA predicted clinically significant ΔSE by 82% [area under the curve(AUC)=0.82] alone, while the value was slightly improved to 85%(AUC=0.85) in combination with axial length and 86%(AUC=0.86) in association with axial length as well as age.CONCLUSION: After cycloplegia with cyclopentolate, the ΔSE decreases with larger LOA, longer axial length and older age. Specifically, LOA plays a more vital role in predicting clinically significant ΔSE.

Estimation of Passenger Car Equivalents for Basic Freeway Sections at Different Traffic Conditions

Passenger car equivalent (PCE) is an important factor which is used to convert traffic volumes containing proportions of heavy good vehicles (HGVs) to a unify measure containing only passenger cars units (PCU). This paper uses large data base of real traffic raw data extracted from loop detector before being aggregated to estimate PCEs. These detectors are located on the M25 and the M42 motorway sites in the United Kingdom. The selected sites represent basic freeway segments as they are far away from the influence of entrance (on ramp) and exit (off ramp) sections. The data are filtered properly so as to estimate passenger car equivalents (PCEs) using lagging headway method for close following situations at different speed ranges. The results suggest that for the same location, the equivalency factors are varies significantly based traffic speed. However, it is proved that such variation with traffic speed is influenced by the differences in lengths between HGVs and cars. Regression models have also been developed linking the PCEs with traffic speed.

On Culture-Bound Words in the Brothers＇ Grimm Fairy Tales and Their Equivalents in English Translations

The aim of the article is to connect the model of cognitive metonymy with the model of types of denotative equivalence highlighting the explanatory potential of the model of cognitive metonymy for describing and clarifying the use and occurrence of word equivalents in the English translations of the Brothers＇ Grimm fairy tales by Margaret Taylor （1914） and Jack Zipes （1987）. The Fairy Tales of the Brothers Grimm （GFT） can be seen in a wide sense as a source of the history of culture and social life in the German speaking countries of the nineteenth century. Culture-bound words refer to a special cultural knowledge, which is in a historical sense not or not completely compatible with the structure of knowledge in our present days, and refer to a common cultural knowledge of the community of German speaking countries as well. This article describes the ways of using English equivalents in the translations of the GFT including lexical and cognitive procedures, which stand behind the use of certain equivalents. This leads to the theoretical question： Is it possible to extend the model of denotative equivalence using features of conceptual metonymy in rendering culture-bound words in the target texts？ Investigating this, there can be established modifications in the theory of conceptual metonymy in the framework of cognitive linguistics.

English-Chinese Phonemic Equivalents Constraints in Transliteration from the Perspective of Optimality Theory

Transliteration aims to adapt loanwords to perfect sound patterns and structures. With the guidance of Optimality Theory, this paper elaborates on the constraints that must be observed in transliteration to achieve Chinese phonological harmony from phonemic equivalents. It analyzes the ranking of constraints for structural acceptability of the loanwords.

The initial stages of Li_(2)O_(2) formation during oxygen reduction reaction in Li-O_(2) batteries:The significance of Li_(2)O_(2) in charge-transfer reactions within devices

Lithium-oxygen batteries are a promising technology because they can greatly surpass the energy density of lithium-ion batteries.However,this theoretical characteristic has not yet been converted into a real device with high cyclability.Problems with air contamination,metallic lithium reactivity,and complex discharge and charge reactions are the main issues for this technology.A fast and reversible oxygen reduction reaction(ORR)is crucial for good performance of secondary batteries',but the partial knowledge of its mechanisms,especially when devices are concerned,hinders further development.From this perspective,the present work uses operando Raman experiments and electrochemical impedance spectroscopy(EIS)to assess the first stages of the discharge processes in porous carbon electrodes,following their changes cycle by cycle at initial operation.A growth kinetic formation of the discharge product signal(Li_(2)O_(2))was observed with operando Raman,indicating a first-order reaction and enabling an analysis by a microkinetic model.The solution mechanism in the evaluated system was ascribed for an equivalent circuit with three time constants.While the time constant for the anode interface reveals to remain relatively constant after the first discharge,its surface seemed to be more non-uniform.The model indicated that the reaction occurs at the Li_(2)O_(2) surface,decreasing the associated resistance during the initial discharge phase.Furthermore,the growth of Li_(2)O_(2) forms a hetero-phase between Li_(2)O_(2)/electrolyte,while creating a more compact and homogeneous on the Li_(2)O_(2)/cathode surface.The methodology here described thus offers a way of directly probing changes in surface chemistry evolution during cycling from a device through EIS analysis.

An Efficient and Odorless Synthesis of Thioethers Using 2-[Bis（alkylthio）methylene]-3-oxo-N-o-tolylbutanamides as Thiol Equivalents

Using 2-[bis（alkylthio）methylene]-3-oxo-N-o-tolylbutanamides 1 as odorless thiol equivalents, an efficient and odorless synthesis of thioethers has been developed. Promoted by NaOH in EtOH, the cleavage of 1 commences to generate thiolate anions, and the generated thiolate anions then react with halides to give various thioethers in good yield. It is noteworthy that only a very faint odor ofthiols can be perceived during both the reaction and the workup.

Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

Deterioration of equivalent thermal conductivity of granite subjected to heating-cooling treatment

Understanding the thermal conductivity of granite is critical for many geological and deep engineering applications.The heated granite was subjected to air-,water-,and liquid nitrogen(LN2-)coolings in this context.The transient hot-wire technique was used to determine the equivalent thermal conductivity(ETC)of the granite before and after treatment.The deterioration mechanism of ETC is analyzed from the meso-perspective.Finally,the numerical model is used to quantitatively study the impact of cooling rate on the microcrack propagation and heat conduction characteristics of granite.The results show that the ETC of granite is not only related to the heating temperature,but also affected by the cooling rate.The ETC of granite decreases nonlinearly with increasing heating temperature.A faster cooling rate causes a greater decrease in ETC at the same heating temperature.The higher the heating temperature,the stronger the influence of cooling rate on ETC.The main explanation for the decrease in ETC of granite is the increase in porosity and microcrack density produced by the formation and propagation of pore structure and microcracks during heating and cooling.Further analysis displays that the damage of granite at the heating stage is induced by the difference in thermal expansion and elastic properties of mineral particles.At the cooling stage,the faster cooling rate causes a higher temperature gradient,which in turn produces greater thermal stress.As a result,it not only causes new cracks in the granite,but also aggravates the damage at the heating stage,which induces a further decrease in the heat conduction performance of granite,and this scenario is more obvious at higher temperatures.

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

Curved-beams can be used to design modular multistable metamaterials(MMMs)with reprogrammable material properties,i.e.,programmable curved-beam periodic structure(PCBPS),which is promising for controlling the elastic wave propagation.The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap,analyze the wave propagation mechanisms,and further form its geometrical and physical criteria for tuning the elastic wave propagation.With the equivalent model,we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability,and investigate the wave propagation characteristics through the PCBPS.To validate the equivalent system,the finite element method(FEM)is employed.It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics.The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

Distribution and correlation of refractive parameters in children with different corneal curvatures in southeast China

AIM:To analyze the distribution of refractive status in school-age children with different corneal curvatures(CC)and the correlation between CC and refractive status.METHODS:A total of 2214 school-aged children of grade 4 in Hangzhou who were screened for school myopia were included.Uncorrected distance visual acuity(UCDVA),non-cycloplegic refraction,axial length(AL),horizontal and vertical corneal curvature(K1,K2)were measured and spherical equivalent(SE),corneal curvature radius(CCR)and axial length/corneal radius of curvature ratio(AL/CR)were calculated.UCDVA<5.0 and SE≤-0.50 D were classified as school-screening myopia.According to the different CCRs,the patients were divided into the lower corneal curvature(LCC)group(CCR≥7.92)and the higher corneal curvature(HCC)group(CCR<7.92).Each group was further divided into the normal AL subgroup and the long AL subgroup.The refractive parameters were compared to identify any differences between the two groups.RESULTS:Both SE and AL were greater in the LCC group(P=0.013,P<0.001).The prevalence of myopia was 38% in the LCC group and 44% in the HCC group(P<0.001).The proportion of children without screening myopia was higher in the LCC group(62%)than in the HCC group(56%).Among these children without screening myopia,the proportion of long AL in the LCC group(24%)was significantly higher than that in the HCC group(0.012%;P<0.001).The change of SE in the LCC group was less affected by the increase of AL than that in the HCC group.CONCLUSION:School-aged children in the LCC group have a lower incidence of screening myopia and longer AL.Low CC can mask SE reduction and AL growth to some extent,and the change of AL growth change more in children with low CC than high CC.Before the onset of myopia,its growth rate is even faster than that after the onset of myopia.

The circuitry landscape of perovskite solar cells:An in-depth analysis

The extensive research and development in perovskite solar cells (PSCs) have rekindled the hopes of converting solar energy into electricity.An elusive understanding of underlying mechanisms is required for the development of efficient PSCs.Over the years,Impedance Spectroscopy (IS) characterization,along with complementary techniques,has proven to be an effective way to understand and analyze the charge transport and recombination at interface and bulk of PSCs.The IS of PSCs have been analyzed,interpreted,and improvised continuously,revealing intricate details about the work.However,there is a lack of centralized source of these details,which make it tougher to account for the generalized approach to understand the device properties.The present work is focused on compiling the research done on various PSC device architectures via IS to construct a comprehensive foundation of information on impedance plots,equivalent circuits,and associated processes.

Dynamic Response of A Group of Cylindrical Storage Tanks with Baffles Considering the Effect of Soil Foundation

The sloshing in a group of rigid cylindrical tanks with baffles and on soil foundation under horizontal excitation is studied analytically.The solutions for the velocity potential are derived out by the liquid subdomain method.Equivalent models with mass-spring oscillators are established to replace continuous fluid.Combined with the least square technique,Chebyshev polynomials are employed to fit horizontal,rocking and horizontal-rocking coupling impedances of soil,respectively.A lumped parameter model for impedance is presented to describe the effects of soil on tank structures.A mechanical model for the soil-foundation-tank-liquid-baffle system with small amount of calculation and high accuracy is proposed using the substructure technique.The analytical solutions are in comparison with data from reported literature and numerical codes to validate the effectiveness and correctness of the model.Detailed dynamic properties and seismic responses of the soil-tank system are given for the baffle number,size and location as well as soil parameter.

Ultrahigh spatiotemporal resolution beam signal reconstruction with bunch phase compensation

Various electromagnetic signals are excited by the beam in the acceleration and beam-diagnostic elements of a particle accelerator.It is important to obtain time-domain waveforms of these signals with high temporal resolution for research,such as the study of beam–cavity interactions and bunch-by-bunch parameter measurements.Therefore,a signal reconstruction algorithm with ultrahigh spatiotemporal resolution and bunch phase compensation based on equivalent sampling is proposed in this paper.Compared with traditional equivalent sampling,the use of phase compensation and setting the bunch signal zero-crossing point as the time reference can construct a more accurate reconstructed signal.The basic principles of the method,simulation,and experimental comparison are also introduced.Based on the beam test platform of the Shanghai Synchrotron Radiation Facility(SSRF)and the method of experimental verification,the factors that affect the reconstructed signal quality are analyzed and discussed,including the depth of the sampled data,quantization noise of analog-to-digital converter,beam transverse oscillation,and longitudinal oscillation.The results of the beam experiments show that under the user operation conditions of the SSRF,a beam excitation signal with an amplitude uncertainty of 2%can be reconstructed.

An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Infiltration,runoff,and slope stability behaviors of infinite slope with macropores based on an improved Green–Ampt model

Infiltration–runoff–slope instability mechanism of macropore slope under heavy rainfall is unclear.This paper studied its instability mechanism with an improved Green–Ampt(GA)model considering the dual-porosity(i.e.,matrix and macropore)and ponding condition,and proposed the infiltration equations,infiltration–runoff coupled model,and safety factor calculation method.Results show that the infiltration processes of macropore slope can be divided into three stages,and the proposed model is rational by a comparative analysis.The wetting front depth of the traditional unsaturated slope is 17.2%larger than that of the macropore slope in the early rainfall stage and 27%smaller than that of the macropore slope in the late rainfall stage.Then,macropores benefit the slope stability in the early rainfall but not in the latter.Macropore flow does not occur initially but becomes pronounced with increasing rainfall duration.The equal depth of the wetting front in the two domains is regarded as the onset criteria of macropore flow.Parameter analysis shows that macropore flow is delayed by increasing proportion of macropore domain(ω_(f)),whereas promoted by increasing ratio of saturated permeability coefficients between the two domains(μ).The increasing trend of ponding depth is sharp at first and then grows slowly.Finally,when rainfall duration is less than 3 h,ωf andμhave no significant effect on the safety factor,whereas it decreases with increasingωf and increases with increasingμunder longer duration(≥3 h).With the increase ofω_(f),the slope maximum instability time advances by 10.5 h,and with the increase ofμ,the slope maximum instability time delays by 3.1 h.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Testing method of rock structural plane using digital drilling

The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evaluating stability and designing supports in underground engineering.Currently,there are no effective testing methods for the characteristic parameters of the rock mass structural plane in underground engineering.The paper presents the digital drilling technology as a new testing method of rock mass structural planes.Flawed rock specimens with cracks of varying widths and angles were used to simulate the rock mass structural planes,and the multifunctional rock mass digital drilling test system was employed to carry out the digital drilling tests.The analysis focuses on the variation laws of drilling parameters,such as drilling pressure and drilling torque,affected by the characteristics of prefabricated cracks,and clarifies the degradation mechanism of rock equivalent compressive strength.Additionally,an identification model for the characteristic parameters of rock mass structural planes during drilling is established.The test results indicate that the average difference of the characteristics of prefabricated cracks identified by the equivalent compressive strength is 2.45°and 0.82 mm,respectively.The identification model while drilling is verified to be correct due to the high identification accuracy.Based on this,a method for testing the characteristic parameters of the surrounding rock structural plane while drilling is proposed.The research offers a theoretical and methodological foundation for precise in situ identification of structural planes of the surrounding rock in underground engineering.

A compact X-band backward traveling-wave accelerating structure

Very high-energy electrons(VHEEs)are potential candidates for FLASH radiotherapy for deep-seated tumors.We proposed a compact VHEE facility based on an X-band high-gradient high-power technique.In this study,we investigated and realized the first X-band backward traveling-wave(BTW)accelerating structure as the buncher for a VHEE facility.A method for calculating the parameters of single cell from the field distribution was introduced to simplify the design of the BTW structure.Time-domain circuit equations were applied to calculate the transient beam parameters of the buncher in the unsteady state.A prototype of the BTW structure with a thermionic cathode-diode electron gun was designed,fabricated,and tested at high power at the Tsinghua X-band high-power test stand.The structure successfully operated with 5-MW microwave pulses from the pulse compressor and outputted electron bunches with an energy of 8 MeV and a pulsed current of 108 mA.

Ice-Induced Vibrational Response of Single-Pile Offshore Wind-Turbine Foundations

Important challenges must be addressed to make wind turbines sustainable renewable energy sources.A typical problem concerns the design of the foundation.If the pile diameter is larger than that of the jacket platform,traditional mechanical models cannot be used.In this study,relying on the seabed soil data of an offshore wind farm,the m-method and the equivalent embedded method are used to address the single-pile wind turbine foundation problem for different pile diameters.An approach to determine the equivalent pile length is also proposed accordingly.The results provide evidence for the effectiveness and reliability of the model based on the equivalent embedded method.