Length Contraction Research Articles

Micro-scale experimental investigation of the effect of pore space deformation on trapping of supercritical CO2

In this study, we investigate the impact of pore space deformation on various trapping mechanisms of supercritical CO2 (scCO2) relevant to storage of CO2 in deep saline aquifers. A series of unsteady-state two-phase brine/scCO2 drainage, imbibition, and dissolution tests were performed on a miniature sandpack sample under various stress conditions. High-resolution x-ray microtomography techniques were employed to acquire the pore and fluid occupancy maps at each step of the experiment, which were subsequently utilized to characterize the pore space deformation and changes in the frequencies of various pore-scale fluid displacement events. Our results revealed that, during the scCO2 injection stage, additional scCO2 was stored in the sandpack sample after the sandpack was compressed due to an increase in the pressure gradient even though the pore volume had decreased. On the other hand, the capillary trapping was impaired by the pore space contraction because all the imbibition displacement mechanisms at the pore scale, including the piston-like advance and snap-off, were facilitated as a consequence of an increase in their threshold capillary pressures. The increased frequency of snap-off events caused additional trapping, but more importantly, displaced scCO2 from throats by fragmenting large residual scCO2 clusters into smaller globules. During the dissolution process, the trapped scCO2 clusters and globules shrank in both pore bodies and throats, resulting in movement of the Main Terminal Meniscus (MTM) interfaces and snap-off events, respectively. The water relative permeability during the dissolution process decreased, at a fixed saturation, with the increase in the effective stress since the small pores occupied by the water phase deformed more significantly than the large pores.

Experimental Refutation of Einstein’s Symmetry Principle

A well-known prediction of the Lorentz transformation (LT) of Einstein’s theory of Special Relativity (SR) is that when two observers exchange light signals, they will both measure a red shift (lowering in frequency). An experiment with gamma rays was reported by Hay et al., in 1960 in which an absorber is mounted at the rim of a high- speed centrifuge while the source is located near the rotor axis. There is general agreement that because of its acceleration, the clock attached to the absorber must be retarded relative to the gamma ray source. Despite the claim that this result is a confirmation of the Symmetry Principle, the fact remains that the slowing down of the absorber clock means that the frequency of the signals it receives from the source will be greater than the standard value, i.e. a blue shift will be observed because more waves are counted per second by virtue of the absorber clock’s reduced rate. This experience therefore stands in direct contradiction of the Symmetry Principle. In addition, it is pointed out that the three space-time predictions of the LT (equal speeds of light, time dilation and FitzGerald length contraction) are incompatible with one another. An alternate theory is presented (Uniform Scaling method) which is in full agreement with the results of the ultra-centrifuge experiment and also avoids any incompatibility with regard to it space-time predictions.

Commuting operators over Pontryagin spaces with applications to system theory

In this paper we extend vessel theory, or equivalently, the theory of overdetermined 2D systems to the Pontryagin space setting. We focus on realization theorems of the various characteristic functions associated to such vessels. In particular, we develop an indefinite version of de Branges-Rovnyak theory over real compact Riemann surfaces. To do so, we use the theory of contractions in Pontryagin spaces and the theory of analytic kernels with a finite number of negative squares. Finally, we utilize the indefinite de Branges-Rovnyak theory on compact Riemann surfaces in order to prove a Beurling type theorem on indefinite Hardy spaces on finite bordered Riemann surfaces.

Measurement quantization

We present principles of Measurement Quantization (MQ) and approaches to measurement that support the discreteness of measure. Several claims are addressed. Notably, that measure is discrete with respect to the internal frame, non-discrete with respect to the system frame and that length is contracted due to the discreteness of measure. We address the relation of angular measure to momentum, the physical significance of count bounds and that the fundamental measures — more precise expressions for Planck’s units — are an emergent property of the internal frame. Quantum experiments by Shwartz, et. al and CODATA provide physical support. We predict and derive values for elementary charge and the gravitational, Hubble, reduced Planck, electric, magnetic, Coulomb, and fine structure constants. We then correlate gravity with electromagnetism (unification). We present expressions for galactic rotation, dark matter, dark energy, and accelerating expansion. MQ advances over Loop Quantum Gravity with two frames, the difference which leads to the physical constants and the laws of nature. We correlate the quantum and cosmological, describing an inflation free quantum epoch, why it ceases and expansion. Therein are solutions to the horizon problem and homogenous, isotropic properties of the universe. Predictions include length contraction unrelated to special or general relativity (SR/GR), 13-digit measures of the gravitational constant, the Planck momentum, and universal mass accretion. A calculation of CMB age, quantity, present-day density and temperature provides additional support. Also offered, discrete solutions to the size and age of the universe, ground state orbital, SR, GR, and equivalence.

Generalized perturbed contractions with related fixed point results

n this paper, we introduce the concept of (F, G)-perturbed contraction in a metric space and we establish some fixed point theorems which extends the results from Branga, A. N. Olaru, I. M. Some Fixed Point Results in Spaces with Perturbed Metrics. Carpathian J. Math. 38 (2022), no. 3, 641–654 and Olaru, I. M.; Secelean, N. A. A new approach of some contractive mappings on metric spaces. Mathematics 9 (2021), 1433. Also, an application to an integral equation and some illustrative examples are given throughout the paper.

A two-experiment finite similitude approach to experimental fluid mechanics

Fluid dynamics experimentation at scale provides an important means of investigation that is presently underpinned by dimensional analysis and computational fluid dynamics (CFD). Unfortunately, despite the obvious success of this twin approach, dimensional analysis provides no solution if scale effects are prevalent and CFD offers reduced practical advantage in the absence of a theory that links information across scaled experiments. This issue is addressed in this paper with the introduction of a new approach to scaled experimentation founded on the theory of finite similitude. Finite similitude is founded on the metaphysical concept of space scaling, where experimental apparatuses, facilities, prototypes, systems, wind tunnels etc., are scaled by the means of space contraction or expansion. There exists no practical means to contract or expand space but what is possible is a mathematical description of space scaling and its impact on governing physics, so providing a means for comparison with scaled systems and real-world experimental behaviours. This paper examines an adaptation of the finite-similitude theory, where two scaled experiments are involved but a second-order version of the theory is applied. All previous work has been limited to zeroth and first-order applications, but in the case of fluid dynamics, second order is shown necessary to capture more accurately convective terms. It is demonstrated in the paper by means of two scaled experiments (designed using second-order theory) that the approach is able to represent behaviours at the full scale that hitherto would have been deemed impossible with traditional dimensional analysis. Numerical and analytical case studies on gravity impacted flows are trialled to illustrate the benefits of the approach with percentage errors reduced from double to single digits.

Dilation Theory and Functional Models for Tetrablock Contractions

A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator T can be dilated to a unitary $${{\mathcal {U}}}$$ , i.e., $$T^n = P_{{\mathcal {H}}}{{\mathcal {U}}}^n|{{\mathcal {H}}}$$ for all $$n =0,1,2,\ldots $$ . A more general multivariable setting for these ideas is the setup where (i) the unit disk is replaced by a domain $$\Omega $$ contained in $${{\mathbb {C}}}^d$$ , (ii) the contraction operator T is replaced by an $$\Omega $$ -contraction, i.e., a commutative operator d-tuple $${{\textbf{T}}}= (T_1, \ldots , T_d)$$ on a Hilbert space $${{\mathcal {H}}}$$ such that $$\Vert r(T_1, \ldots , T_d) \Vert _{{{\mathcal {L}}}({{\mathcal {H}}})} \le \sup _{\lambda \in \Omega } | r(\lambda ) |$$ for all rational functions with no singularities in $$\overline{\Omega }$$ and the unitary operator $${{\mathcal {U}}}$$ is replaced by an $$\Omega $$ -unitary operator tuple, i.e., a commutative operator d-tuple $${{\textbf{U}}}= (U_1, \ldots , U_d)$$ of commuting normal operators with joint spectrum contained in the distinguished boundary $$b\Omega $$ of $$\Omega $$ . For a given domain $$\Omega \subset {\mathbb C}^d$$ , the rational dilation question asks: given an $$\Omega $$ -contraction $${{\textbf{T}}}$$ on $${{\mathcal {H}}}$$ , is it always possible to find an $$\Omega $$ -unitary $${{\textbf{U}}}$$ on a larger Hilbert space $${{\mathcal {K}}}\supset {{\mathcal {H}}}$$ so that, for any d-variable rational function without singularities in $${\overline{\Omega }}$$ , one can recover r(T) as $$r(T) = P_{{\mathcal {H}}}r({{\textbf{U}}})|_{{\mathcal {H}}}$$ . We focus here on the case where $$\Omega = {{\mathbb {E}}}$$ , a domain in $${{\mathbb {C}}}^3$$ called the tetrablock. (i) We identify a complete set of unitary invariants for a $${{\mathbb {E}}}$$ -contraction (A, B, T) which can then be used to write down a functional model for (A, B, T), thereby extending earlier results only done for a special case, (ii) we identify the class of pseudo-commutative $${{\mathbb {E}}}$$ -isometries (a priori slightly larger than the class of $${{\mathbb {E}}}$$ -isometries) to which any $${{\mathbb {E}}}$$ -contraction can be lifted, and (iii) we use our functional model to recover an earlier result on the existence and uniqueness of a $${{\mathbb {E}}}$$ -isometric lift $$(V_1, V_2, V_3)$$ of a special type for a $${{\mathbb {E}}}$$ -contraction (A, B, T).

Fixed Point Results via Real-Valued Function Satisfying Integral Type Rational Contraction

In this article, we mainly discuss the existence and uniqueness of fixed point satisfying integral type contractions in complete metric spaces via rational expression using real-valued functions. We improve and unify many widely known results from the literature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we conclude with an example presented graphically in favour of our work.

Fixed Point for Almost Contractions in v-Generalized b-Metric Spaces

We present a significant example to show that the class of v-generalized b-metric spaces properly contains the class of v-generalized metric spaces as well as b-metric spaces. This is accomplished because the example provided by Došenović et al. (2020) is insufficient to expose the generality of v-generalized b-metric spaces over the existing related spaces. Therefore, we establish fixed point theorems by defining generalized almost contractions of rational type and Reich type in v-generalized b-metric spaces. Moreover, we compare the proven results with the already existing fixed point theorems in this space by presenting suitable examples. As a consequence of these fixed point theorems, we further develop some common fixed-point results that ensure the existence and uniqueness of coincidence points and common fixed points for a pair of self maps. Finally, we use the outcome to check that the given Fredholm integral equation has a solution and that it is also unique.

The Schrödinger-Korteweg-de Vries system on the half-line

Using the Fokas unified transform method (UTM), the well-posedness of the initial-boundary value problem (ibvp) for the Schrödinger-Korteweg-de Vries system on the half-line is studied for initial data (u0,v0)(x) in spatial Sobolev spaces Hs1(0,∞)×Hs2(0,∞), s1>0, s2>−3/4, and boundary data (g0,h0)(t) in the temporal Sobolev spaces suggested by the time regularity of the Cauchy problem for the corresponding linear system. First, linear estimates in Bourgain spaces are derived by utilizing the Fokas solution formula of the ibvp for the forced linear system. Then, using these and the needed bilinear/trilinear estimates, it is shown that the iteration map defined by the Fokas solution formula is a contraction in an appropriate solution space.

Best proximity point for generalized proximal contraction in a complete metric space

In this article, we have proved some best proximity point theorems for a non-self mapping by using generalized proximal contraction in a complete metric space. An example is also given in the support of our result.

Fever of Unknown Origin and Multidrug Resistant Organism Colonization in AML Patients.

Colonization by multidrug-resistant organisms (MDRO) is a frequent complication in hematologic departments, which puts patients at risk of life-threatening bacterial sepsis. Fever of unknown origin (FUO) is a condition related to the delivery of chemotherapy in hematologic malignancies, in which the use of antibiotics is debated. The incidence, risk factors, and influence on the outcome of these conditions in patients with acute myeloid leukemia (AML) are not clearly defined. We retrospectively analyzed 132 consecutive admissions of non-promyelocytic AML patients at the Hematology Unit of the University Tor Vergata in Rome between June 2019 and February 2022. MDRO swab-based screening was performed in all patients on the day of admission and once weekly after that. FUO was defined as fever with no evidence of infection. Of 132 consecutive hospitalizations (69 AML patients), MDRO colonization was observed in 35 cases (26%) and resulted independently related to a previous MDRO colonization (p=0.001) and length of hospitalization (p=0.03). The colonization persistence rate in subsequent admissions was 64%. MDRO-related bloodstream infection was observed in 8 patients (23%) and correlated with grade III/IV mucositis (p=0.008) and length of hospitalization (p=0.02). FUO occurred in 68 cases (51%) and correlated with an absolute neutrophilic count <500μ/L at admission (0.04). In our experience, MDRO colonization is a frequent and difficult-to-eradicate condition that can arise at all stages of treatment. Prompt discharge of patients as soon as clinical conditions allow could limit the spread of MDRO. In addition, the appropriate use of antibiotics, especially in the case of FUO, and the contraction of hospitalization length, when feasible, are measures to tackle the further spread of MDRO.

Fixed-points of interpolative Kannan type contractions in bipolar metric spaces

Fixed-points of interpolative Kannan type contractions in bipolar metric spaces

Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces

&lt;abstract&gt; &lt;p&gt;A contemporary fuzzy technique is employed in the current study to generalize some established and recent findings. For researchers, fixed point (FP) procedures are highly advantageous and appealing mechanisms. Discovering fuzzy fixed points of fuzzy mappings (FM) meeting Nadler's type contraction in complete fuzzy metric space (FMS) and?iri? type contraction in complete metric spaces (MS) is the core objective of this research. The outcomes are backed up by example and applications that highlight these findings. There are also preceding conclusions that are given as corollaries from the relevant literature. In this mode, numerous consequences exist in the significant literature are extended and combined by our findings.&lt;/p&gt; &lt;/abstract&gt;

ТРАНСФОРМАЦИЯ ГОРОДСКОГО ПРОСТРАНСТВА АРХАНГЕЛЬСКА

The emergence of a city, the creation of its infrastructure, and the population growth depend on many factors, but of decisive importance are the main city-forming functions. With time, the value of such functions changes, they can disappear. This primarily concerns industrial cities. If there are no other sources for growth, the urban space begins to transform under the influence of the closure of industrial enterprises, reduction of the population. This is often expressed in contraction and degradation of the city areas being released from their functions. This is a problem for many cities around the world in the context of the changing economic paradigm and transition to a post-industrial economy. Arkhangelsk is an example of a city that was gradually involved in performing various functions from its foundation, but the main growth of its urban space began with the development of the timber industry complex. The modern reduction of available forest resources led to the closure of numerous enterprises of the timber industry, which threatens the existence of villages created around these enterprises. The author conducted a retrospective analysis of the urban space formation and transformation in Arkhangelsk, identified the main areas that have lost their former functions and are degrading. The quality of the environment was assessed by the cost of housing in the city districts, its territorial disproportions in peripheral and central areas were identified. A study of the population dynamics showed a partial contraction of urban space, manifested in the gradual loss of population in former timber mill settlements, especially those located on islands. The city is losing territories that became its part due to Soviet industrialization. The author analyzes the prospects for the development of the urban space basing on the study of the general plan of Arkhangelsk.

On Some Novel Fixed Point Results for Generalized -Contractions in�Metric-Like Spaces with Application

The focus of our work is on the most recent results in fixed point theory related to contractive mappings. We describe variants of -contractions that expand, supplement and unify an important work widely discussed in the literature, based on existing classes of interpolative and -contractions. In particular, a large class of contractions in terms of and F for both linear and nonlinear contractions are defined in the framework of -metric-like spaces. The main result in our paper is that --weak contractions have a fixed point in -metric-like spaces if function F or the specified contraction is continuous. As an application of our results, we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

Common fixed point theorems of integral type contraction in cone metric space

Common fixed point theorems of integral type contraction in cone metric space

Some common fixed point theorems in bipolar metric spaces and applications

&lt;abstract&gt;&lt;p&gt;In this article, we prove some common fixed point theorems for generalized rational type contractions in bipolar metric spaces. These theorems also generalize and extend several interesting results of metric fixed point theory to the bipolar metric context. In addition, we provide some examples to illustrate our theorems, and applications are obtained in areas of homotopy theory and integral equations by using iterative methods for mathematical operators on a bipolar metric space.&lt;/p&gt;&lt;/abstract&gt;

A new approach to generalized interpolative proximal contractions in non archimedean fuzzy metric spaces

&lt;abstract&gt;&lt;p&gt;We introduce a new type of interpolative proximal contractive condition that ensures the existence of the best proximity points of fuzzy mappings in the complete non-archimedean fuzzy metric spaces. We establish certain best proximity point theorems for such proximal contractions. We improve and generalize the fuzzy proximal contractions by introducing fuzzy proximal interpolative contractions. The obtained results improve and generalize the best proximity point theorems published in Fuzzy Information and Engineering, 5 (2013), 417–429. Moreover, we provide many nontrivial examples to validate our best proximity point theorem.&lt;/p&gt;&lt;/abstract&gt;

Hardy-Rogers type contraction in double controlled metric-like spaces

&lt;abstract&gt;&lt;p&gt;In this paper, we establish a new fixed point result for Hardy-Rogers type contractions in double controlled metric-like spaces. Our result generalizes many important theorems in the literature. We will provide an example to illustrate our results.&lt;/p&gt;&lt;/abstract&gt;