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According to the fact that the single function transformation which can both reduce the class ratio dispersion and keep the relative error no enlargement after the inverse transformation does not exist, this paper provides the separable binary function transformation F(x(k),k)=f(x(k))⋅g(k). The authors select the appropriate f(x(k)) and g(k) to get F(x(k),k)=f(x(k))⋅g(k). The sequence {F(x(k),k)}k=1n can not only improve the modeling accuracy but also ensure that the inverse transformation relative error has no enlargement.

First of all, to meet that the sequence reduces the class ratio dispersion after binary function transformation, the sufficient and necessary condition of binary function transformation with reduced class ratio dispersion is obtained. Secondly, to meet the condition that the inverse transformation relative error is not enlarged, the necessary condition of separable binary function transformation is obtained respectively for monotonically increasing and monotonically decreasing function f(x). Finally, the feasibility and correctness of this method are illustrated by example analysis and application.

The sufficient and necessary condition of binary function transformation with reduced class ratio dispersion and the necessary condition of separable binary function transformation with the inverse transformation relative error no enlargement.

According to the properties of separable binary function transformation provided in this paper, the grey prediction function model is established, which can improve the modeling accuracy.

This paper provides a binary function transformation, and researches the sufficient and necessary condition of binary function transformation with reduced class ratio dispersion and the necessary condition of separable binary function transformation with the inverse transformation relative error no enlargement. It is easy for scholars to carry out the pretest before selecting the separable binary function transformation. The binary function transformation is the further extension of single function transformation, which broadens and enriches the choice of function transformation.

This paper sets out to solve a common and crucial fundamental theoretical problem of gray incidence cluster analysis: to [X]={X|ρ(X,Y)≥1−ε0} constitute an approximate classification, it must first be proven that [X]={X|ρ(X,Y)=1} constitutes a rigorous classification.

This paper does not study the concrete expressions of various incidence degrees but rather the perfect correlation essence of such incidence degrees, that is, sufficient and necessary conditions.

For any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree, it is proven that the perfect correlation relation is an equivalence relation. The set composed of all sequences Y that are equivalent to sequences X is studied, that is, the equivalence class of X. The structure and mutual relations of these equivalence classes are discussed, and the topological homeomorphism concept of incidence degree is introduced. The conclusion is obtained that the equivalence classes of the two incidence degrees must be the same when the topological homeomorphism is obtained.

In this paper, only the perfect correlation relation of any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree are studied as equivalent relations.

Not only are the research results of several incidence degrees involved in this paper original but also many other effective incidence degrees have not done this basic research, so this paper opens up a research direction with theoretical significance.

This paper aims to propose and demonstrate a novel surface plasmon resonance (SPR)-sensing approach by using the fundamental mode beam based on a graded index multimode fiber (GIF). The proposed SPR sensor has high sensitivity and controllable working dynamic range, which expects to solve the two bottlenecks of fiber SPR sensor, including low sensitivity and the difficulty in multichannel detection.

The low-order mode of the GIF to SPR sense, which keeps the sensitivity advantage of the single-mode fiber SPR sensor, is used. By using this new SPR sensor, the effect of light incident angle and gold film thickness on working dynamic range was studied. According to the study results, the smaller is the incident angle, the larger is the SPR working dynamic range and the longer is the resonance wavelength with a fixed gold film thickness; the larger is the gold film thickness, the longer is the resonance wavelength with a fixed grinding angle. After the parameter optimization, the sensitivity of these two parameter-adjusting methods reach 4,442 and 3031 nm/RIU.

When the grinding angle of the GIF increases, the dynamic range of the resonance wavelength increases and has a redshift, sensitivity increases, and the resonance valley becomes more unobvious with a fixed gold film thickness. Similarly, when gold film thickness increases, the dynamic range of the resonance wavelength increases and has a redshift, sensitivity increases, and the resonance valley becomes more unobvious with a fixed grinding angle. These adjusting performance aforementioned lay the foundation for solving of the fiber-based SPR multichannel detection and increasing of the fiber-based SPR sensor sensitivity, which has a good application value.

This paper aims to clarify the relationship between the performance of the metal nanoparticles and the sensitivity of the fiber surface plasma resonance (SPR) sensor. It proposes modeling the sensing effects of a single-mode fiber SPR sensor with a cone angle structure decorated with metal nanoparticles. This study uses the metal nanoparticles to the realize enhanced sensitivity of refractive index sensing.

This paper opted for an exploratory study using a simulation approach of finite-difference time-domain (FDTD). Specifically, the effect of size, the material and the shape of the metal nanoparticle on sensing performance are investigated theoretically.

In conclusion, it is evident that the localized SPR (LSPR) effect weakens as the diameter of the gold nanosphere increases, the SPR effect enhances and the SPR sensitivity increases first and then decreases. The metal nanoparticle with the different materials and different shapes also have different LSPR and SPR sensitivity and wavelength length dynamic range. The investigation shows that, by changing parameters, the reflection spectra of the fiber SPR sensor exhibit an obvious transition from LSPR to SPR characteristics, and enhanced sensitivity of the refractive index is realized.

This paper fulfills an identified need to study how the sensitivity of the fiber SPR sensor can be enhanced by the metal nanoparticle. After the optimization of parameters, the sensitivity of 5,140 nm/RIU is achieved, which provides a new research direction for sensitivity enhancement of fiber SPR sensor.

The purpose of this paper is to study the dynamic behavior of complex-valued switched grey neural network models (SGNMs) with distributed delays when the system parameters and external input are grey numbers.

Firstly, by using the properties of grey matrix, M-matrix theory and Homeomorphic mapping, the existence and uniqueness of equilibrium point of the SGNMs were discussed. Secondly, by constructing a proper Lyapunov functional and using the average dwell time approach and inequality technique, the robust exponential stability of the SGNMs under restricted switching was studied. Finally, a numerical example is given to verify the effectiveness of the proposed results.

Sufficient conditions for the existence and uniqueness of equilibrium point of the SGNMs have been established; sufficient conditions for guaranteeing the robust stability of the SGNMs under restricted switching have been obtained.

(1) Different from asymptotic stability, the exponential stability of SGNMs which include grey parameters and distributed time delays will be investigated in this paper, and the exponential convergence rate of the SGNMs can also be obtained; (2) the activation functions, self-feedback coefficients and interconnected matrices are with different forms in different subnetworks; and (3) the results obtained by LMIs approach are complicated, while the proposed sufficient conditions are straightforward, which are conducive to practical applications.

This paper aims to study the sensitivity enhancement effect of the gold nanorod on fiber surface plasmon resonance (SPR) sensor. It proposes modeling the sensing effects of fiber SPR sensor decorated with metal nanoparticles. By using simulation and experiment, the sensitivity enhancement effect of the gold nanorod was studied and demonstrated.

The paper opted for an exploratory study using simulation approach of finite-difference time-domain. Specifically, the effect of ratios and aspect ratios of gold nanorod on sensing performance are investigated theoretically. Based on the mathematical models, the validation experiments by using the gold nanorod with the aspect ratios of 5.1 were done to verify the sensitivity enhancement effect of the gold nanorod.

In conclusion, it is evident that with the increases of the aspect ratios, the sensing sensitivity of the refractive index increases first, then gradually stabilizes or decreases. After parameter optimization, the ratios and aspect ratios of gold nanorod are chosen to be 8 nm and 12.5, respectively, which makes the optimal refractive index sensitivity of 4465.53 nm/RIU be realized. In addition, the validation experiments by using the gold nanorod with the aspect ratios of 5.1 verify the sensitivity enhancement effect of the gold nanorods.

This paper proposes and demonstrates a new method for the sensitivity enhancement of fiber SPR sensor. After parameter optimization, the maximum sensitivity of 4465.53 nm/RIU was achieved by using 8 nm gold nanorods with the aspect ratios of 12.5. To verify the sensitivity enhancement of the gold nanorods, the authors also did the validation experiments. The testing results indicated that after the decoration of the gold nanorods, the sensitivity of the sensing probe increases from 2190.57 nm/RIU to 2693.24 nm/RIU, which demonstrates the sensitivity enhancement effect of the gold nanorods.

The construction industry has actively attempted to tackle the low-productivity issues arising from inefficient construction planning. It is imperative to understand how construction practitioners perceive technology integration in construction planning in light of emerging technologies. This study intended to uncover unique experimental findings by integrating 4D-building information modelling (BIM) to virtual reality (VR) technology during construction planning among construction professionals at light steel framing (LSF) projects.

The building industry participants were invited to provide inputs on two different construction planning methods: conventional and innovative methods. The conventional method involved the participants using traditional platforms such as 2D computer-aided design (CAD) and physical visualisation of paper-based construction drawings for the LSF assembly process with a Gantt Chart tool to complete construction planning-related tasks for the targeted project. Comparatively, participants are required to perform the same tasks using more innovative platforms like 4D-BIM in a VR environment.

A Charrette Test Method was used to validate the findings, highlighting an improvement in usability (+10.3%), accuracy (+89.1%) and speed (+30%) using 4D BIM with VR compared to the conventional paper-based method. The findings are also validated by a paired t-test, which is supported by the rationality of the same findings. This study posits positive results for construction planning through the utilisation of modern practices and technologies. These findings are significant for the global construction industry facing low productivity issues, delays and certainty in terms of building delivery timelines due to poor construction planning.

This new blend of technologies—combining 4D BIM and VR in industrialised construction projects—potentially directs future initiatives to drive the efficiency of construction planning in the building lifecycle. The interactive BIM-based virtual environment would purposefully transform construction planning practices in order to deliver modern and more certain building construction methods with a focus on prefabrication processes.

This paper discusses the idea of projecting corporate image in terms of culturally regulated codes of appeals by using, mainly, the examples of ad campaigns by some US business companies in the post‐9/11 environment. The image of patriotism those companies are aspiring to suggests corporate imagery can be a shared social phenomenon, i.e. collective ethos, thus raising questions about the traditional approach to corporate imagery, which is summarized as “self‐representation.” The way to build up collective ethos is through Burke’s “identification,” seen as both a strategy and goal of communication. The paper also provides an overview of rhetorical theory on using image as a presentation strategy to explore the reason why it has been treated in history as a way for self‐projection, or representation of a “corporate self.”

The purpose of this paper is to introduce the new class ratio dispersion, the new smooth degree sequence and the comparison criterion of the new smooth degree and to propose the new prior check of grey modeling in order to meet the modeling demand of the optimized grey models which have the white exponential law of coincidence.

This paper introduces the corresponding new concepts and new comparison criterion which can reflect the approach degree of the raw data and the normal geometric progression by analogy with the traditional class ratio dispersion, smooth degree sequence and comparison criterion.

To the optimized grey models, the new concepts and the new comparison criterion can be regarded as the prior check of grey modeling.

First, the new concepts and the new comparison criterion can reflect the approach degree of the raw data and the normal geometric progression, and this paper proposes the prior check of grey modeling to the optimized grey models. Second, this paper proposes the quantificational valuation criterion – the concept of the smooth degree which can reflect the approach degree of a single sequence and the normal geometric progression, and ends the status quo that there is only the comparison criterion of the smooth degree between two sequences but not the quantificational valuation criterion of a single sequence.

The purpose of this paper is to discuss the necessary condition of the relative error between continuous function transformation after inverse transformation and original sequence is not larger than the relative error between transformed sequence and its corresponding simulation sequence.

First, explore the function transformation feature of after inverse transformation the relative error not enlarged, then combine this feature with the function transformation feature of not enlarge the class ratio dispersion, not reduce the smoothness which author have got, and obtain a kind of special transformation that not enlarge class ratio dispersion, not reduce the smoothness and after inverse transformation keep the relative not enlarged. Meanwhile, offer the concrete form of this special function type to monotone increasing continuous function transformation and monotone decreasing continuous function transformation, respectively, and study its properties.

This paper finds the concise and important feature of monotonically increasing function transformation after inverse transformation whether the relative error enlarge or not is at first, the concise and important feature of monotonically decreasing function transformation after inverse transformation relative error not enlarged is. And find that the ideal function transformation which both reduces class ratio dispersion strictly and keeps error of inverse transformation not enlarged is non-exist for monotone increasing function transformation and monotone decreasing function transformation.

Use the necessary condition given by this paper, it may use to judge whether function transformation can keep relative error of inverse transformation not enlarged by easy data calculation before build modeling, therefore, choose the best function transformation. These results tell the authors: the paper cannot treat any functions as the same that whether the relative error of inverse transformation will not enlarge (or not reduced), but the authors should divide them into two parts to discuss that it will be expanded in some range or be reduced in some range. It will affect the future direction of the research, not to find the function transform both satisfies the class ratio dispersion reduced and keep the relative error of inverse transformation not enlarged, but to study which kind of function transform will narrow class ratio dispersion in some range, after the modeling accuracy improvement, but after the inverse transformation the relative error enlarged, and at this time the simulation accuracy is still higher than the simulation accuracy of original data modeling directly. Which kind of function transform will expand class ratio dispersion in some range, after the modeling accuracy diminution, but after the inverse transformation the relative error not enlarged, and now the simulation accuracy is still higher than the simulation accuracy of original data modeling directly, too.

Let peers no longer spend energy in seeking the function transformation which both reduce class ratio dispersion and keep relative error of inverse transformation not enlarged. At the same time, also remind peers that even if a function transformation reduces class ratio dispersion greatly, the data modeling accuracy improves a lot after transformation, but the error of inverse transformation is may quite large, still. Besides, even if function transformation increases class ratio dispersion, the data modeling accuracy is not good after transformation, the ideal situation after inverse transformation would occur, and the possibility cannot be excluded.