Cyclically Interval Total Coloring of the One Point Union of Cycles

A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union ?of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles? and? are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.

Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles

A total coloring of a graph G is a functionsuch that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. A k-interval is a set of k consecutive integers. A cyclically interval total t-coloring of a graph G is a total coloring a of G with colors 1,2,...,t, such that at least one vertex or edge of G is colored by i,i=1,2,...,t, and for any, the set is a -interval, or is a -interval, where dG(x) is the degree of the vertex x in G. In this paper, we study the cyclically interval total colorings of cycles and middle graphs of cycles.

A NEW METHOD FOR STRESS ANALYSIS OF A CYCLICALLY SYMMETRIC STRUCTURE

In this paper, a computational method for finite element stress analysis of a cyclically symmetric structure subjected to arbitrary loads is provided. At first, using discrete Fourier transformation technique, the complete structure is analyzed by considering only one sector with appropriate complex constraints on its boundary with the adjacent sectors. Next, an imaginary structure which is composed of two identically overlapping sectors is constructed, and that the complex constraints mentioned above can be equivalently replaced by a set of real constraints on this imaginary structure is proved. Therefore, the stress analysis of a cyclically symmetric structure can be solved conveniently by most of finite element programs.

Super Cyclically Edge Connected Half Vertex Transitive Graphs

Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.

On a Number of Colors in Cyclically Interval Edge Colorings of Simple Cycles

A proper edge t-coloring of a graph G is a coloring of its edges with colors 1,2,???,t such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each its vertex x, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. For an arbitrary simple cycle, all possible values of t are found, for which the graph has a cyclically interval t-coloring.

Note on Cyclically Interval Edge Colorings of Simple Cycles

A proper edge t-coloring of a graph G is a coloring of its edges with colors 1, 2,..., t, such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each vertex, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. In this paper, we provide a new proof of the result on the colors in cyclically interval edge colorings of simple cycles which was first proved by Rafayel R. Kamalian in the paper “On a Number of Colors in Cyclically Interval Edge Colorings of Simple Cycles, Open Journal of Discrete Mathematics, 2013, 43-48”.

Experimental study of hollow rectangular bridge column performance under vertical and cyclically bilateral loads

To investigate the seismic performance of hollow reinforced concrete （RC） bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges （JTG/T B02-01-2008）. The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns.

Testing and modeling of cyclically loaded rock anchors

The Norwegian Public Roads Administration(NPRA) is planning for an upgrade of the E39 highway route at the westcoast of Norway. Fixed links shall replace ferries at seven fjord crossings. Wide spans and large depths at the crossings combined with challenging subsea topography and environmental loads call for an extension of existing practice. A variety of bridge concepts are evaluated in the feasibility study. The structures will experience significant loads from deadweight, traffic and environment. Anchoring of these forces is thus one of the challenges met in the project. Large-size subsea rock anchors are considered a viable alternative. These can be used for anchoring of floating structures but also with the purpose of increasing capacity of fixed structures. This paper presents first a thorough study of factors affecting rock anchor bond capacity. Laboratory testing of rock anchors subjected to cyclic loading is thereafter presented. Finally, the paper presents a model predicting the capacity of a rock anchor segment, in terms of a ribbed bar, subjected to a cyclic load history. The research assumes a failure mode occurring in the interface between the rock anchor and the surrounding grout. The constitutive behavior of the bonding interface is investigated for anchors subjected to cyclic one-way tensile loads. The model utilizes the static bond capacity curve as a basis, defining the ultimate bond sbuand the slip s1 at τ. A limited number of input parameters are required to apply the model. The model defines the bond-slip behavior with the belonging rock anchor capacity depending on the cyclic load level(τcy/τ), the cyclic load ratio(R= τcy/τcy), and the number of load cycles(N). The constitutive model is intended to model short anchor lengths representing an incremental length of a complete rock anchor.

VECTORIAL EKELAND VARIATIONAL PRINCIPLE AND CYCLICALLY ANTIMONOTONE EQUILIBRIUM PROBLEMS

In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.

Damage evolution of rock-encased-backfill structure under stepwise cyclic triaxial loading

Rock-encased-backfill(RB)structures are common in underground mining,for example in the cut-andfill and stoping methods.To understand the effects of cyclic excavation and blasting activities on the damage of these RB structures,a series of triaxial stepwise-increasing-amplitude cyclic loading experiments was conducted with cylindrical RB specimens(rock on outside,backfill on inside)with different volume fractions of rock(VF=0.48,0.61,0.73,and 0.84),confining pressures(0,6,9,and 12 MPa),and cyclic loading rates(200,300,400,and 500 N/s).The damage evolution and meso-crack formation during the cyclic tests were analyzed with results from stress-strain hysteresis loops,acoustic emission events,and post-failure X-ray 3D fracture morphology.The results showed significant differences between cyclic and monotonic loadings of RB specimens,particularly with regard to the generation of shear microcracks,the development of stress memory and strain hardening,and the contact forces and associated friction that develops along the rock-backfill interface.One important finding is that as a function of the number of cycles,the elastic strain increases linearly and the dissipated energy increases exponentially.Also,compared with monotonic loading,the cyclic strain hardening characteristics are more sensitive to rising confining pressures during the initial compaction stage.Another finding is that compared with monotonic loading,more shear microcracks are generated during every reloading stage,but these microcracks tend to be dispersed and lessen the likelihood of large shear fracture formation.The transition from elastic to plastic behavior varies depending on the parameters of each test(confinement,volume fraction,and cyclic rate),and an interesting finding was that the transformation to plastic behavior is significantly lower under the conditions of 0.73 rock volume fraction,400 N/s cyclic loading rate,and 9 MPa confinement.All the findings have important practical implications on the ability of backfill to support underground excavations.

Liquefaction susceptibility and deformation characteristics of saturated coral sandy soils subjected to cyclic loadings-a critical review

Coral sandy soils widely exist in coral island reefs and seashores in tropical and subtropical regions.Due to the unique marine depositional environment of coral sandy soils,the engineering characteristics and responses of these soils subjected to monotonic and cyclic loadings have been a subject of intense interest among the geotechnical and earthquake engineering communities.This paper critically reviews the progress of experimental investigations on the undrained behavior of coral sandy soils under monotonic and cyclic loadings over the last three decades.The focus of coverage includes the contractive-dilative behavior,the pattern of excess pore-water pressure(EPWP)generation and the liquefaction mechanism and liquefaction resistance,the small-strain shear modulus and strain-dependent shear modulus and damping,the cyclic softening feature,and the anisotropic characteristics of undrained responses of saturated coral sandy soils.In particular,the advances made in the past decades are reviewed from the following aspects:(1)the characterization of factors that impact the mechanism and patterns of EPWP build-up;(2)the identification of liquefaction triggering in terms of the apparent viscosity and the average flow coefficient;(3)the establishment of the invariable form of strain-based,stress-based,or energy-based EPWP ratio formulas and the unique relationship between the new proxy of liquefaction resistance and the number of cycles required to reach liquefaction;(4)the establishment of the invariable form of the predictive formulas of small strain modulus and strain-dependent shear modulus;and(5)the investigation on the effects of stress-induced anisotropy on liquefaction susceptibility and dynamic deformation characteristics.Insights gained through the critical review of these advances in the past decades offer a perspective for future research to further resolve the fundamental issues concerning the liquefaction mechanism and responses of coral sandy sites subjected to cyclic loadings associated with seismic events in marine environments.

Enhancing capacitive deionization performance and cyclic stability of nitrogen-doped activated carbon by the electro-oxidation of anode materials

Electrode materials with high desalination capacity and long-term cyclic stability are the focus of capacitive deionization(CDI) community. Understanding the causes of performance decay in traditional carbons is crucial to design a high-performance material. Based on this, here, nitrogen-doped activated carbon(NAC) was prepared by pyrolyzing the blend of activated carbon powder(ACP) and melamine for the positive electrode of asymmetric CDI. By comparing the indicators changes such as conductivity, salt adsorption capacity, pH, and charge efficiency of the symmetrical ACP-ACP device to the asymmetric ACP-NAC device under different CDI cycles, as well as the changes of the electrochemical properties of anode and cathode materials after long-term operation, the reasons for the decline of the stability of the CDI performance were revealed. It was found that the carboxyl functional groups generated by the electro-oxidation of anode carbon materials make the anode zero-charge potential(E_(pzc)) shift positively,which results in the uneven distribution of potential windows of CDI units and affects the adsorption capacity. Furthermore, by understanding the electron density on C atoms surrounding the N atoms, we attribute the increased cyclic stability to the enhanced negativity of the charge of carbon atoms adjacent to quaternary-N and pyridinic-oxide-N.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Ionization Engineering of Hydrogels Enables Highly Efficient Salt‑Impeded Solar Evaporation and Night‑Time Electricity Harvesting

Interfacial solar evaporation holds immense potential for brine desalination with low carbon footprints and high energy utilization.Hydrogels,as a tunable material platform from the molecular level to the macroscopic scale,have been considered the most promising candidate for solar evaporation.However,the simultaneous achievement of high evaporation efficiency and satisfactory tolerance to salt ions in brine remains a challenging scientific bottleneck,restricting the widespread application.Herein,we report ionization engineering,which endows polymer chains of hydrogels with electronegativity for impeding salt ions and activating water molecules,fundamentally overcoming the hydrogel salt-impeded challenge and dramatically expediting water evaporating in brine.The sodium dodecyl benzene sulfonate-modified carbon black is chosen as the solar absorbers.The hydrogel reaches a ground-breaking evaporation rate of 2.9 kg m−2 h−1 in 20 wt%brine with 95.6%efficiency under one sun irradiation,surpassing most of the reported literature.More notably,such a hydrogel-based evaporator enables extracting clean water from oversaturated salt solutions and maintains durability under different high-strength deformation or a 15-day continuous operation.Meantime,on the basis of the cation selectivity induced by the electronegativity,we first propose an all-day system that evaporates during the day and generates salinity-gradient electricity using waste-evaporated brine at night,anticipating pioneer a new opportunity for all-day resource-generating systems in fields of freshwater and electricity.

Fatigue properties and damage constitutive model of salt rock based on CT scanning

To investigate the macroscopic fatigue properties and the mesoscopic pore evolution characteristics of salt rock under cyclic loading,fatigue tests under different upper-limit stresses were carried out on salt rock,and the mesoscopic pore structures of salt rock before and after fatigue tests and under different cycle numbers were measured using CT scanning instrument.Based on the test results,the effects of the cycle number and the upper-limit stress on the evolution of cracks,pore morphology,pore number,pore volume,pore size,plane porosity,and volume porosity of salt rock were analyzed.The failure path of salt rock specimens under cyclic loading was analyzed using the distribution law of plane porosity.The damage variable of salt rock under cyclic loading was defined on basis of the variation of volume porosity with cycle number.In order to describe the fatigue deformation behavior of salt rock under cyclic loading,the nonlinear Burgers damage constitutive model was further established.The results show that the model established can better reflect the whole development process of fatigue deformation of salt rock under cyclic loading.

Emerging mechanisms and implications of c GAS-STING signaling in cancer immunotherapy strategies

The intricate interplay between the human immune system and cancer development underscores the central role of immunotherapy in cancer treatment.Within this landscape,the innate immune system,a critical sentinel protecting against tumor incursion,is a key player.The cyclic GMP-AMP synthase(c GAS)and stimulator of interferon genes(STING)pathway has been found to be a linchpin of innate immunity:activation of this signaling pathway orchestrates the production of type I interferon(IFN-α/β),thus fostering the maturation,differentiation,and mobilization of immune effectors in the tumor microenvironment.Furthermore,STING activation facilitates the release and presentation of tumor antigens,and therefore is an attractive target for cancer immunotherapy.Current strategies to activate the STING pathway,including use of pharmacological agonists,have made substantial advancements,particularly when combined with immune checkpoint inhibitors.These approaches have shown promise in preclinical and clinical settings,by enhancing patient survival rates.This review describes the evolving understanding of the c GAS-STING pathway's involvement in tumor biology and therapy.Moreover,this review explores classical and non-classical STING agonists,providing insights into their mechanisms of action and potential for optimizing immunotherapy strategies.Despite challenges and complexities,the c GAS-STING pathway,a promising avenue for enhancing cancer treatment efficacy,has the potential to revolutionize patient outcomes.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Failure transition of shear-to-dilation band of rock salt under triaxial stresses

Great potential of underground gas/energy storage in salt caverns seems to be a promising solution to support renewable energy.In the underground storage method,the operating cycle unfortunately may reach up to daily or even hourly,which generates complicated pressures on the salt cavern.Furthermore,the mechanical behavior of rock salt may change and present distinct failure characteristics under different stress states,which affects the performance of salt cavern during the time period of full service.To reproduce a similar loading condition on the cavern surrounding rock mass,the cyclic triaxial loading/unloading tests are performed on the rock salt to explore the mechanical transition behavior and failure characteristics under different confinement.Experimental results show that the rock salt samples pre-sent a diffused shear failure band with significant bulges at certain locations in low confining pressure conditions(e.g.5 MPa,10 MPa and 15 MPa),which is closely related to crystal misorientation and grain boundary sliding.Under the elevated confinement(e.g.20 MPa,30 MPa and 40 MPa),the dilation band dominates the failure mechanism,where the large-size halite crystals are crushed to be smaller size and new pores are developing.The failure transition mechanism revealed in the paper provides additional insight into the mechanical performance of salt caverns influenced by complicated stress states.

Plasticity of photorespiratory carbon concentration mechanism in Sedobassia sedoides(Pall.)Freitag&G.Kadereit under elevated CO_(2)concentration and salinity

Rising atmospheric CO_(2)(carbon dioxide)concentrations and salinization are manifestations of climate change that affect plant growth and productivity.Species with an intermediate C_(3)-C_(4)type of photosynthesis live in a wide range of precipitation,temperature,and soil quality,but are more often found in warm and dry habitats.One of the intermediate C_(3)-C_(4)photosynthetic type is C_(2)photosynthesis with a carbon concentration mechanism(CCM)that reassimilates CO_(2)released via photorespiration.However,the ecological significance under which C_(2)photosynthesis has advantages over C_(3)and C_(4)plants remains largely unexplored.Salt tolerance and functioning of CCM were studied in plants from two populations(P1 and P2)of Sedobassia sedoides(Pall.)Freitag&G.Kadereit Asch.species with C_(2)photosynthesis exposed to 4 d and 10 d salinity(200 mM NaCl)at ambient(785.7 mg/m^(3),aCO_(2)and elevated(1571.4 mg/m^(3),eCO_(2))CO_(2).On the fourth day of salinity,an increase in Na+content,activity catalase,and superoxide dismutase was observed in both populations.P2 plants showed an increase in proline content and a decrease in photosynthetic enzyme content:rubisco,phosphoenolpyruvate carboxylase(PEPC),and glycine decarboxylase(GDC),which indicated a weakening of C_(2)and C_(4)characteristics under salinity.Treatment under 10 d salinity led to an increased Na^(+)content and activity of cyclic electron flow around photosystem I(PSI CEF),a decreased content of K^(+)and GDC in both populations.P1 plants showed greater salt tolerance,which was assessed by the degree of reduction in photosynthetic enzyme content,PSI CEF activity,and changes in relative growth rate(RGR).Differences between populations were evident under the combination of eCO_(2)and salinity.Under long-term salinity and eCO_(2),more salt-tolerant P1 plants had a higher dry biomass(DW),which was positively correlated with PSI CEF activity.In less salt-tolerant P2 plants,DW correlated with transpiration and dark respiration.Thus,S.sedoides showed a high degree of photosynthetic plasticity under the influence of salinity and eCO_(2)through strengthening(P1 plants)and weakening C_(4)characteristics(P2 plants).

Effect of NaCl Concentration on the Cumulative Strain and Pore Distribution of Clay under Cyclic Loading

Clay,as the most common soil used for foundationfill,is widely used in various infrastructure projects.The phy-sical and mechanical properties of clay are influenced by the pore solution environment.This study uses a GDS static/dynamic triaxial apparatus and nuclear magnetic resonance experiments to investigate the effects of cyclic loading on clay foundations.Moreover,the development of cumulative strain in clay is analyzed,and afitting model for cumulative plastic strain is introduced by considering factors such as NaCl solution concentration,con-solidation stress ratio,and cycle number.In particular,the effects of the NaCl solution concentration and con-solidation stress ratio on the pore distribution of the test samples before and after cyclic loading are examined,and the relationship between microscopic pore size and macroscopic cumulative strain is obtained accordingly.Our results show that as the consolidation stress ratio grows,an increasing number of large pores in the soil samples are transformed into small pores.As the NaCl solution concentration becomes higher,the number of small pores gradually decreases,while the number of large pores remains unchanged.Cyclic loading causes the disappearance of the large pores in the samples,and the average pore size before cyclic loading is posi-tively correlated with the axial cumulative strain after cyclic loading.The cumulative strain produced by the soil under cyclic loading is inversely proportional to the NaCl solution concentration and consolidation stress ratio.