Aperiodic Research Articles

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism.

Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity

Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity

Evolutionary Period Changes for 52 Cataclysmic Variables, and the Failure for the Most-fundamental Prediction of the Magnetic Braking Model

The evolution of cataclysmic variables (CVs) is driven by period changes ( Ṗ ), for which the long-venerable consensus is the magnetic braking model (MBM). The MBM has its only distinctive assumption being a power-law “recipe” describing the angular momentum loss (AML) in the binary, producing a single unique evolutionary track with Ṗ as a function of the orbital period. This required prediction can be used to test the most-fundamental assumption of MBM, but it has never been tested previously. In this paper, I collect Ṗ measures for 52 CVs of all types. First, 44% of the CVs have positive Ṗ , with such being impossible in MBM. Second, even among the CVs with negative Ṗ , their Ṗ measures are always more negative than required by MBM, with an average deviation of 110×. Third, three CVs have large chaotic variations in Ṗ that are impossible for MBM, proving that some unknown mechanism exists and is operating that dominates for these systems. Fourth, the MBM does not account for the long-term effects on evolution arising from the large sudden period decreases seen across many nova events, with this unaccounted effect dominating for the majority of nova systems and changing the sign of the overall evolutionary Ṗ . Fifth, three recurrent novae are observed to suddenly change Ṗ by an order of magnitude across a nova event, with this being impossible in the MBM. In all, the required MBM Ṗ predictions all fail for my 52 CVs, usually by orders of magnitude, so the MBM AML-recipe is wrong by orders of magnitude.

Ground State Solutions for a Non-Local Type Problem in Fractional Orlicz Sobolev Spaces

In this paper, we study the following non-local problem in fractional Orlicz–Sobolev spaces: (−ΔΦ)su+V(x)a(|u|)u=f(x,u), x∈RN, where (−ΔΦ)s(s∈(0,1)) denotes the non-local and maybe non-homogeneous operator, the so-called fractional Φ-Laplacian. Without assuming the Ambrosetti–Rabinowitz type and the Nehari type conditions on the non-linearity f, we obtain the existence of ground state solutions for the above problem with periodic potential function V(x). The proof is based on a variant version of the mountain pass theorem and a Lions’ type result in fractional Orlicz–Sobolev spaces.

[Two kinds of percutaneous endoscopic lumbar decompression in the treatment of single level lumbar lateral recess stenosis].

To prospectively compare the clinical efficacy and radiographic outcomes between interlaminar percutaneous endoscopic lumbar decompression(IL-PELD) and transforaminar percutaneous endoscopic lumbar decompression(TF-PELD) in the treatment of single-segment lumbar lateral recess stenosis. From April 2018 to July 2021, 85 patients with single-segment lumbar lateral recess stenosis underment percutaneous endoscopic lumbar decompression.There were 44 males and 41 females, aged from 49 to 81 years old with an average of (65.5±8.3) years old, duration of lumbar lateral recess stenosis ranging from 3 to 83 months with an average of (26.7±16.5) months. They were divided into IL-PELD group and TF-PELD group according to the different operation methods. There were 47 patients in the IL-PELD group, including 28 males and 19 females aged from 50 to 80 yeaes old with an average age was (66.7±9.3) years old. The disease duration ranged from 3 to 65 months with an average of (25.7±15.0) months. There were 38 patients in the TF-PELD group, including 16 males and 22 females, aged from 51 to 78 years old with an average of(64.1±7.6) years old. The disease duration ranged from 4 to 73 months with an average of (27.9±18.3) months The operation time, intraoperative blood loss, intraoperative fluoroscopy, hospitalization day and complications of the two groups were recorded. Visual analogue scale (VAS) to evaluate low back pain and lower limb pain, Oswestry disability index(ODI) to evaluate lumbar function in preoperative and postoperative period(1month, 6 months and last follow-up)were recorded. the sagittal diameter of the lateral recess of the responsible intervertebral space in preoperative and 1 week after the operation were recorded. The operation was successfully completed in both groups without serious complications such as vascular injury, dural sac tear and nerve injury. The operation time in IL-PED group(69.3±19.3)min was significantly longer than that in TF-PELD group(57.5±14.5)min (P<0.05). There was no significant difference in the intraoperative blood loss between the two groups (P>0.05). The number of intraoperative fluoroscopy in TF-PELD group (8.8±2.6)times was significantly higher than that in IL-PED group(4.8±1.2)times (P<0.05). The hospitalization days of the two groups were not statistically significant (P>0.05). VAS for low back and lower extremity pain and ODI were (5.1±2.2), (6.9±1.3) scores and (71.4±12.6) % in IL-PELD group, and (4.7±1.8), (6.9±1.3) scores and (68.4±13.9)% in TF-PELD group. In the IL-PELD group, the VAS of low back pain was (2.4±1.5), (1.6±0.8), (1.4±0.9) scores, and the VAS of lower extremity pain was (3.0±1.2), (1.6±0.7), (1.5±1.0) scores, ODI was (32.6±11.9) %, (17.4±6.5) %, (19.3±9.3)%;In TF-PELD group, the VAS of low back pain was (2.6±1.4), (1.5±0.6), (1.4±1.0) scores, and the VAS of lower extremity pain was (2.8±1.2), (1.6±0.6), (1.5±1.2) scores, The ODI was (32.0±11.2) %, (15.0±6.1) %, and (20.0±11.3) %. The VAS and ODI of the two groups at each time point after operation were significantly improved compared with those before operation (P<0.05), but there was no statistically significant difference between the groups (P>0.05), and there was no statistically significant difference in the interaction between different time points and groups (P>0.05). At 1 week after operation, the sagittal diameter of lateral recess in both groups was significantly increased compared with that before operation (P<0.05), but there was no significant difference between the two groups at each time point (P>0.05). According to the modified Macnab criteria, IL-PELD group was rated as excellent in 24 cases, good in 19 cases and fair in 4 cases. In TF-PELD group the results were excellent in 19 cases, good in 15 cases, fair in 3 cases and poor in 1 case. There was no significant difference between the two groups (P>0.05). IL-PELD and TF-PELD can expand the lateral recess in the treatment of single level lumbar lateral recess stenosis, and have achieved good clinical effects.

Spectral stability of periodic traveling wave solutions for a double dispersion equation

ABSTRACT In this article, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method, we find explict periodic waves and we also present a characterization for all positive and periodic solutions for the model using the monotonicity of the period map in terms of the energy levels. The monotonicity of the period map is also useful to obtain the quantity and multiplicity of non-positive eigenvalues for the associated linearized operator and to do so, we use tools of the Floquet theory. Finally, we prove the spectral stability by analyzing the difference between the number of negative eigenvalues of a convenient linear operator restricted to the space constituted by zero-mean periodic functions and the number of negative eigenvalues of the matrix formed by the tangent space associated to the low order conserved quantities of the evolution model.

Home indoor air quality and cognitive function over one year for people working remotely during COVID-19

The coronavirus disease 2019 (COVID-19) pandemic triggered an increase in remote work-from-home for office workers. Given that many homes now function as offices despite not being designed to support office work, it is critical to research the impact of indoor air quality (IAQ) in homes on the cognitive performance of people working from home. In this study, we followed 206 office workers across the U.S. over one year under remote or hybrid-remote settings during 2021–2022. Participants placed two real-time, consumer-grade indoor environmental monitors in their home workstation area and bedroom. Using a custom smartphone application geofenced to their residential address, participants responded to surveys and periodic cognitive function tests, including the Stroop color–word interference test, Arithmetic two-digit addition/subtraction test, and Compound Remote Associates Task (cRAT). Exposures assessed included carbon dioxide (CO2) and thermal conditions (indoor heat index: a combination of temperature and relative humidity) averaged over 30 min prior to each cognitive test. In fully adjusted longitudinal mixed models (n ≤ 121), we found that indoor thermal conditions at home were associated with cognitive function outcomes non-linearly (p < 0.05), with poorer cognitive performance on the Stroop test and poorer creative problem-solving on the cRAT when conditions were either too warm or too cool. Most indoor CO2 levels were <640 ppm, but there was still a slight association between higher CO2 and poorer cognitive performance on Stroop (p = 0.09). Our findings highlight the need to enhance home indoor environmental quality for optimal cognitive function during remote work, with benefits for both employees and employers.

Numerical simulation of a thermal energy storage system using sunrise and sunset transient temperature models

The temperature of the sun was modeled in this study using two transient solar temperature equations for sunrise and sunset that were developed for designing a latent heat thermal energy storage (LHTES) system for a concentrated solar power (CSP) plant. The derivation of the equations was based on the existing solar hour angle and the fundamental periodic function equations. Ansys' computational fluid dynamics code was used to investigate numerically the transient response of the conjugate melting and solidification of a phase change material (PCM) in a cylindrical shell and helical heat pipe (HHP) thermal system. The models for both equations were applied as user-defined functions (UDFs). The heat transfer medium was air. The predicted liquid and solid fractions provide quantitative data on the temperature and the stored solar energy. The effectiveness of both models in enhancing heat transfer and their suitability as real-time transient solar temperature models in heat transfer engineering is demonstrated by comparisons between their outputs. With high agreement, experimental data from the open literature was used to validate the numerical model's predictions. The solar temperature models aim to contribute to heat transfer enhancement for a reduced PCM energy storage time in designing a high-temperature solar thermal storage that is adequate to maintain a steady supply of electricity and energy for domestic and commercial applications and to accelerate the global transition to low-carbon energy.

$$(\mu _{1},\mu _{2})$$-Pseudo-asymptotically $$\tau $$-periodic function applied to models for differential equations with delays

$$(\mu _{1},\mu _{2})$$-Pseudo-asymptotically $$\tau $$-periodic function applied to models for differential equations with delays

The stability of smooth solitary waves for the [formula omitted]-family of Camassa–Holm equations

The b-family of Camassa–Holm (b-CH) equation is a one-parameter family of PDEs, which includes the completely integrable Camassa–Holm and Degasperis–Procesi equations but possesses different Hamiltonian structures. Motivated by this, we study the existence and the orbital stability of the smooth solitary wave solutions with nonzero constant background to the b-CH equation for the special case b=1, whose the Hamiltonian structure is different from that of b≠1. We establish a connection between the stability criterion for the solitary waves and the monotonicity of a singular integral along the corresponding homoclinic orbits of the spatial ODEs. We verify the latter analytically using the framework for the monotonicity of period function of planar Hamiltonian systems, which shows that the smooth solitary waves are orbitally stable. In addition, we find that the existence and orbital stability results for 0<b<1 are similar to that of b>1, particularly the stability criteria are the same. Finally, combining with the results for the case b>1, we conclude that the solitary waves to the b-CH equation is structurally stable under the variation of the parameter b>0.

Cognitive behavioural therapy for depression, quality of life, and cognitive function in the post-stroke period: systematic review and meta-analysis.

The post-stroke period is associated with a lot of sequelae, including depression, decreased quality of life, and decline of cognitive function. Apart from the pharmacotherapy, it is also important to find a non-pharmacological treatment to relieve the sequelae. Cognitive behavioural therapy (CBT) might be a potential candidate, which can be clarified by a systematic review and meta-analysis. The eligible criteria of enrolled studies in the systematic review and meta-analysis were the randomised clinical trials (RCTs) using CBT to treat post-stroke depression, or with the focus on quality of life or cognitive function in the post-stroke period. The endpoint scores of depression, quality of life, and cognitive function scales were the targeted outcome for the final meta-analysis in the random effects model. Ten RCTs with 432 post-stroke patients receiving CBT and 385 controls were included. The meta-analysis results showed significant improvements in depression severity and quality of life. However, no significant difference between CBT and control groups was found in cognitive function. In addition, significant heterogeneity was derived from the meta-analysis. According to the meta-analysis results, CBT might be beneficial for relieving depression severity and improving quality of life. However, cognitive function might not be influenced by CBT. Further studies with a more consistent CBT design with greater sample sizes should be warranted to clarify and confirm the treatment effects of CBT for post-stroke depression and quality of life.

Solitary and Periodic Wave Solutions of Fractional Zoomeron Equation

The Zoomeron equation plays a significant role in many fields of physics, especially in soliton theory, such as helping to reveal new distinctive properties in different physical phenomena such as fluid dynamics, laser physics, and nonlinear optics. By using the Riccati–Bernoulli sub-ODE approach and the Backlund transformation, we search for soliton solutions of the fractional Zoomeron nonlinear equation. A number of solutions have been put forth, such as kink, anti-kink, cuspon kink, lump-type kink solitons, single solitons, and others defined in terms of pseudo almost periodic functions. The (2 + 1)-dimensional fractional Zoomeron equation given in a form undergoes precise dynamics. We use the computational software, Matlab 19, to express these solutions graphically by changing the value of various parameters involved. A detailed analysis of their dynamics allows us to obtain completely better insights necessarily with the elementary physical phenomena controlled by the fractional Zoomeron equation.

Representations of groups on Banach spaces

We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let G \mathcal {G} be a topological group, and A \mathcal {A} a unital symmetric C ∗ C^* -subalgebra of U C ( G ) \mathrm {UC}(\mathcal {G}) , the algebra of bounded uniformly continuous functions on G \mathcal {G} . Generalizing the notion of a stable metric, we study A \mathcal {A} -metrics δ \delta , i.e., the function δ ( e , ⋅ ) \delta (e, \cdot ) belongs to A \mathcal {A} ; the case A = W A P ( G ) \mathcal {A}=W\hskip -0.7mm A\hskip -0.2mm P(\mathcal {G}) , the algebra of weakly almost periodic functions on G \mathcal {G} , recovers stability. If the topology of G G is induced by a left invariant metric d d , we prove that A \mathcal {A} determines the topology of G \mathcal {G} if and only if d d is uniformly equivalent to a left invariant A \mathcal {A} -metric. As an application, we show that the additive group of C [ 0 , 1 ] C[0,1] is not reflexively representable; this is a new proof of Megrelishvili [Topological transformation groups: selected topics, Elsevier, 2007, Question 6.7] (the problem was already solved by Ferri and Galindo [Studia Math. 193 (2009), pp. 99–108] with different methods and later the results were generalized by Yaacov, Berenstein, and Ferri [Math. Z. 267 (2011), pp.129–138]). Let now G \mathcal {G} be a metric group, and assume A ⊆ L U C ( G ) \mathcal {A}\subseteq \mathrm {LUC}(\mathcal {G}) , the algebra of bounded left uniformly continuous functions on G \mathcal {G} , is a unital C ∗ C^* -algebra which is the uniform closure of coefficients of representations of G \mathcal {G} on members of F \mathscr {F} , where F \mathscr {F} is a class of Banach spaces closed under ℓ 2 \ell _2 -direct sums. We prove that A \mathcal {A} determines the topology of G \mathcal {G} if and only if G \mathcal {G} embeds into the isometry group of a member of F \mathscr {F} , equipped with the weak operator topology. As applications, we obtain characterizations of unitary and reflexive representability.

Hot Jupiter Diversity and the Onset of TiO/VO Revealed by a Large Grid of Non-Grey Global Circulation Models

Abstract The population of hot Jupiters is extremely diverse, with large variations in their irradiation, period, gravity and chemical composition. To understand the intrinsic planet diversity through the observed population level trends, we explore the a-priori scatter in the population created by the different responses of atmospheric circulation to planetary parameters. We use the SPARC/MITgcm 3D global circulation model to simulate 345 planets spanning a wide range of instellation, metallicity, gravity and rotation periods typical for hot Jupiters, while differentiating between models with and without TiO/VO in their atmosphere. We show that the combined effect of the planetary parameters leads to a large diversity in the ability of atmospheres to transport heat from day-side to night-side at a given equilibrium temperature. We further show that the hot-spot offset is a non-monotonic function of planetary rotation period and explain our findings by a competition between the rotational and divergent parts of the circulation. As a consequence, hot-spot offset and phase curve amplitude are not necessarily correlated. Finally, we compare the observables from our grid to the population of Spitzer and Hubble observations of hot Jupiters. We find that the sudden jump in brightness temperature observed in the Spitzer secondary eclipse measurements can be naturally explained by the cold-trapping of TiO/VO at approximately 1800K. The grid of modelled spectra, phase curves and thermal structures are made available to the community, together with a python code for visualization of the grid properties, at DOI:10.5281/zenodo.10785321 and http://sim3d.oca.eu/.

Extraction of optical wave structures to the coupled fractional system in magneto-optic waveguides

In this article, truncated M-fractional coupled nonlinear Schrodinger equation (NLSE) with quadratic–cubic nonlinearity is under observation. The studied model is composed of chromatic dispersion, magneto-optic parameter and inter-modal dispersion. The NLSE is the most significant physical model to explain the fluctuations of optical soliton proliferation. The NLSEs have become more popular because of the clarity with which they explain a wide range of complex physical phenomena and the depth with which they display dynamical patterns via localized wave solutions. Optical soliton propagation in magneto-optic is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. The optical solitons are secured in the forms of bright, dark, singular and combo solitons. In addition, hyperbolic, periodic and exponential function solutions have been recovered. The modified Sardar subequation and enhanced modified extended tanh-expansion approaches recently developed integration tools are adopted in this study for securing the solutions. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The effect of parameters have been observed by allotting suitable values and sketching the different shapes of the graphs.

Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions

In this paper, the inverse spectral problem method is used to integrate a nonlinear sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin equations and the first trace formula satisfies sine-Gordon-type equations with an additional term.

Meromorphic Solutions of Nonlinear Differential-Difference Equations Involving Periodic Functions

Meromorphic Solutions of Nonlinear Differential-Difference Equations Involving Periodic Functions

Evaluation of reaction rate of thermogravimetric analysis data using periodic sinc function interpolation

AbstractThe periodic sinc function interpolation offers a compelling solution to address the issue of noise in the analysis of thermogravimetric analysis (TGA) data, thereby enhancing the outcomes of differential techniques such as the Friedman isoconversional method. In this study, we introduce a novel approach that leverages the periodic sinc function interpolation to directly obtain smooth reaction rates from TGA data, eliminating the reliance on numerical differentiation methods. The efficacy of this method has been confirmed through its application to noisy experimental data derived from the thermal decomposition of various polymers, showcasing its robustness. Readers are provided with the corresponding code for Gnu Octave, serving as a free alternative to MATLAB. Additionally, the activation energies calculated from the experimental data using both the Friedman method and periodic sinc function interpolation closely align with those determined by the integral Vyazovkin method, emphasizing the validity and reliability of this new approach.

Approximation of Periodic Functions by Wavelet Fourier Series

This paper aims to examine the expansion of periodic functions using wavelet bases. M. Skopina [8] obtained a Wavelet analog of the classical Jackson’s theorem for trigonometric approximation. Our result generalizes the result of M. Skopina [8] and V. Karanjgaokar et al. [15].

Physics-inspired transfer learning for ML-prediction of CNT band gaps from limited data

Recent years have seen a drastic increase in the scientific use of machine learning (ML) techniques, yet their applications remain limited for many fields. Here, we demonstrate techniques that allow overcoming two obstacles to the widespread adoption of ML, particularly relevant to nanomaterials and nanoscience fields. Using the prediction of the band gap values of carbon nanotubes as a typical example, we address the representation of the periodic data as well as training on extremely small datasets. We successfully showed that careful choice of the activation function allows capturing periodic tendencies in the datasets that are common in physical data and previously posed significant difficulty for neural networks. In particular, utilization of the recently proposed parametric periodic Snake activation function shows a dramatic improvement. Furthermore, tackling a typical lack of accurate data, we used the transfer learning technique utilizing more abundant low-quality computational data and achieving outstanding accuracy on a significantly expanded dataspace. This strategy was enabled by the use of a combination of the Snake and ReLU layers, capturing data periodicity and amplitude, respectively. Hence, retraining only ReLU layers allowed the transfer of the periodic tendencies captured from low-quality data to the final high-accuracy neural network. Those techniques are expected to expand the usability of ML approaches in application to physical data in general and the fields of nanomaterials in particular.