Miracle-dz/UniFAR-FTUs huggingface dataset:
Induced Representations of Locally Compact Groups II. The Frobenius Reciprocity Theorem

In the study of the relationship between the representation theory of a group and those of its various subgroups an important role is played by Frobenius's notion of induced representation. To every representation L of the subgroup G of the finite group 65 there is assigned a well defined representation UL of ( called the representation of M induced by L. In I of this series [10] the author began a systematic study of a generalization of this notion in which (5 is a separable locally compact topological group and the spaces of L and UL are possibly infinite dimensional Hilbert spaces. In particular [10] contains a generalization of the Frobenius reciprocity theorem; that is the theorem asserting that UL contains the irreducible representation M of (D just as many times as the restriction of M to G contains the irreducible representation L of G. The generalization contained in [10] is unsatisfactory in that it deals only with the discrete finite dimensional irreducible components of the representations concerned and becomes vacuous when these representations decompose in a continuous fashion or have no finite dimensional irreducible components. A more satisfactory generalization has been obtained by Mautner [13, 14]. It deals in a consequent fashion with continuously decomposable representations of 5 but is restricted by the requirement that G be compact. This means in particular that only discretely decomposable representations of G need be dealt with. The principal result of the present article is a generalization of the Frobenius reciprocity theorem which deals effectively with continuously decomposable representations of both M and G. Since in compensation for the hypothesis that G be compact, we require that both G and 5 have regular representations which are of type I, our theorem does not quite include that of Mautner. However we show in addition that whenever the regular representation of G is not only of type I but also discretely decomposable then the requirement that the regular representation of (M be of type I can be eliminated. Thus our methods also yield a result which includes that of Mautner. In neither of our results is it necessary to assume that the groups concerned are unimodular. A noteworthy feature of our principal theorem is that it includes a reciprocity not only for the multiplicities but for the measures involved in the continuous decompositions as well. The basic idea in our approach is a new proof of the Frobenius reciprocity theorem in the finite case which has the advantage of generalizing significantly
Effect of ultraviolet exposure and palm fibre/fibreglass direction on composite

Composite can be used as an alternatif material to replace items made of wood. Wood usually not resist to water and prone to weathering in outdoor application. Composite is expected to overcome the weakness of wood. This research aims to make composite with different direction of palm fibre/fibreglass as filler and unsaturated polyester resin as matrix with hand lay-up method, also to find out whether its suitable for outdoor application or not. Ultraviolet (UV) exposure is one of element at outdoor environment that can damage polymer matrix composite. UV exposure for 1, 2 and 3 months was carried out on composites with different palm fibre directions: unidirectional, bidirectional and random. To find significant relationship
Do Minimum Wages Reduce Employment? Some Empirical Evidence from Bangladesh

Minimum wage policy is practiced in many countries with the intention of establishing a wage floor for low-wage workers having less bargaining power in the labour market. However, there is some evidence that such well-intended policy might have adverse effects on employment. This study employs a basic model where firm level employment data for a sample of 27 firms for the period 2000-2015 is used to analyse the effects of changes in minimum wage on employment in the readymade garments industry in Bangladesh. The main results suggest that higher minimum wages result in higher formal employment, particularly female employment, in these firms. The major policy implication of the study is to support the enforcement of suitable regulation to ensure competitive and fair wages as well as workers welfare.
Urolithiasis Symptoms and Risk Factors Among the General Population of Alahsa, Saudi Arabia

Objective: This study aims to assess the awareness and attitudes about urolithiasis among the general population of Alahsa, Saudi Arabia. Methodology: A cross-sectional study was conducted in September 2022 in Alahsa, Saudi Arabia, using a validated questionnaire that was distributed to the general population. Inclusion criteria include male and female citizens of Saudi Arabia who were living in Alahsa, older than 18 years old, and willing to participate in the study. Exclusion criteria include non-Saudi citizens or Saudi citizens who did not live in Alahsa. Data were analyzed using SPSS Statistics. Result: The results showed there were 1023 participants. The results showed the awareness level of symptoms associated with kidney stones at 29%, complications at 34%, diagnosis at 51%, and treatment at 16%. The results showed there was a significant association between a history of kidney stones and having no complications (p-value = 0.002) or inflammation (p-value = 0.009). However, there was no significant association between kidney stone symptoms and the participants' comorbidities. Conclusion: According to our findings, there was a low level of knowledge about the condition and the methods to prevent it, like dietary and lifestyle modifications. Regardless of the low level of general knowledge, there was some awareness of urolithiasis in some elements. Therefore, it is advised to increase health awareness campaigns.
A Rankine source method solution of a ﬁnite depth,wave-body interaction problem

A Rankine source method is developed adopting continuous free surface and seabed source panel distributions to solve numerically wave-body interaction problems involving various seabed conditions. The free surface and seabed surface proﬁles are represented by continuous panels rather than a discretization by isolated points. These panels are positioned exactly on the ﬂuid boundary surfaces and the proposed method does not require a desingularization technique. For a two-dimensional forced oscillatory body problem, the inﬂuences of a ﬂat, concave or convex/hump shaped seabed at diﬀerent water depths are investigated. Both heave and sway motions are examined and the accuracy and eﬃciency of the numerical solutions are validated by comparison with published numerical predictions and, where possible, experimental data. Through these simulated ﬁndings, the inﬂuences of uneven seabeds on the hydrodynamic characteristics associated with wave-body interaction problems are discussed.
Mathematical study of quantum and classical models for random materials in the atomic scale

The contributions of this thesis concern two topics. The ﬁrst part is dedicated to the study of mean-ﬁeld models for the electronic structure of materials with defects. In Chapter 2, we introduce and study the reduced Hartree-Fock (rHF) model for disordered crystals. We prove the existence of a ground state and establish, for (short-range) Yukawa interactions, some properties of this ground state. In Chapter 3, we consider crystals with extended defects. Assuming Yukawa interactions, we prove the existence of an electronic ground state, solution of the self-consistent ﬁeld equation. We also investigate the case of crystals with low concentration of random defects. In Chapter 4, we present some numerical results obtained from the simulation of one-dimensional random systems. In the second part, we consider multiscale-in-time kinetic Monte Carlo models. We prove, for the three models presented in Chapter 6, that in the limit of large time-scale separation, the slow variables converge to an eﬀective dynamics. Our results are illustrated by numerical simulations.
HUBUNGAN SANITASI LINGKUNGAN, HIGIENE PERORANGAN DENGAN KEJADIAN DIARE PADA BALITA DI WILAYAH KERJA PUSKESMAS LAINEA KABUPATEN KONAWE SELATAN

Penyakit diare merupakan penyakit yang ditandai dengan berubahnya bentuk tinja dengan intensitas buang air besar secara berlebihan (lebih dari 3 kali dalam kurun waktu satu hari). Data Puskesmas Lainea menunjukkan tahun 2016 terdapat 444 penderita diare, tahun 2017 terdapat 298, tahun 2018 terdapat 418 dan tahun 2019 sebanyak 243 penderita kasus terhitung dari bulan januari-september. Berdasarkan dari data puskesmas Lainea jumlah penderita diare pada balita yang tertinggi dibandingkan kecamatan yang lain di Kabupaten Konawe Selatan. Penelitian ini bertujuan untuk mengetahui hubungan sanitasi lingkungan (penyediaan air bersih, penggunaan jamban, tempat pembuangan sampah, Saluran Pembuangan Air Limbah (SPAL) dan higiene perorangan (kebiasaan mencuci tangan dan pengelolaan makanan) dengan kejadian kejadian diare pada balita di wilayah kerja Puskesmas Lainea Kabupaten Konawe Selatan Tahun 2019. Penelitian ini menggunakan teknik penarikan sampel proportional random sampling. Populasi pada penelitian ini berjumlah 2.347 balita, besar sampel berjumlah 142 balita. Hasil dari penelitian ini menunjukan bahwa tidak ada hubungan yang bermakna antara penyediaan air bersih dengan kejadian diare (p-value= 1,000 >0,05), tidak ada hubungan yang bermakna antara penggunaan jamban dengan kejadian diare (p-value = 0,524 >0,05), ada hubungan yang bermakna antara tempat pembuangan sampah dengan kejadian diare (p-value = 0,014<0,05), ada hubungan yang bermakna antara saluran pembuangan air limbah (SPAL) dengan kejadian diare (p-value = 0,028<0,05), tidak ada hubungan yang bermakna antara kebiasaan mencuci tangan dengan kejadian diare (p-value = 0,188>0,05), tidak ada hubungan yang bermakna antara pengelolaan makanan dengan kejadian diare (p-value = 0,337>0,05). Kesimpulan dalam penelitian ini yaitu ada hubungan antara tempat pembuangan sampah, saluaran pembuangan air limbah (SPAL) dengan kejadian diare, dan tidak ada hubungan antara penyediaan air bersih, penggunaan jamban, kebiasaan mencuci tangan, pengelolaan makanan dengan kejadian diare
Coupling Quantified Bodies

The main promise behind the idea of self-quantification is to transform our lives through the continuous collection of numerical evidence about the body and its activity. Although this process may help boost self-knowledge, everyday life also involves a complex network of relations with other bodies that exert a significant, sometimes determining, influence on our behaviour. To address this concern, we suggest that self-quantification data can be modulated as perturbations to other human and non-human bodies that, in turn, may directly affect the everyday practices of the self. By coupling quantified bodies, we transform existing practices by disrupting the elements that realise, perform and reproduce existing practices. In order to explore and further understand the affective potential of this idea, we designed a system that creates unfamiliar, digitally enabled couplings between two quantified bodies: a human and a plant. In particular, in this design experiment we modulate walking activity data into perturbations to a quantified plant. How does this coupling transform the way we look at self-quantification? Are we bringing forth a new space of responsibility and ethical concern? What if the plant dies because someone did not walk enough? In this article we discuss the implications of creating such a coupling keeping a critical distance to current forms of self-quantification, which are often focused on change through prescriptive solutions rather than through the fostering of self-determined growth. With this work we aim to expand the current understanding of the affective possibilities of self-quantification in the context of social change.
Evaluation of bean residues in the production of agglomerated panels

This work aimed to evaluate the physical-mechanical properties of Pinus oocarpa wood agglomerated panels produced with different levels (0 %, 25 %, 50 %, 75 % and 100 %) of wood replacement with bean residues. For this purpose, Pinus oocarpa wood and the agricultural residue were reduced into particles and their properties of apparent density, extractives, lignin and ash content of these raw materials were determined. Then, the particles were dried to a 3 % humidity and granulometrically selected to produce panels with a den - sity of 0,60 g/cm 3 . These particles were bonded using 12 % urea-formaldehyde adhesive, pressed, following normative dimensions (250 mm x 250 mm x 15 mm (width, length, and thickness)), and kept in a climate-con - trolled environment (20 ºC ± 2 ºC and 65 % ± 5 % RH) until the physical and mechanical tests were carried out. The research results indicated that the particles from bean residues in comparison with Pinus oocarpa wood, presented low density, lignin and holocellulose values, and higher extractives data. Furthermore, regarding the characterization of the panels, there was a trend towards uniformity in the apparent density values, an increase in the properties of compact ratio, water absorption and thickness swelling, and a decrease in their mechanical properties associated with the increase in the by-product addition to the panels. Therefore, new studies are necessary, seeking a larger study and greater knowledge of the addition effects of bean residues in particulate panels, aiming the dissemination of this sustainable process on large scale.
Flaws In The Big Bang Point ToGENESIS ,A New Millennium Model Of The Cosmos: Part 4 — How Will The Scientific Community React To Big Bang's Vast Nonconservation-of-Energy Losses?

In 1936 Hubble expressed his concern about astronomical redshifts and energy conservation: “Obviously since the product [energy × wavelength] remains constant, redshifts, by increasing wavelengths, must reduce the energy in the quanta. Any plausible interpretation of redshifts must account for the loss of energy. ” The scientific community rightly expects that big-bang cosmology resolved this concern consistent with energy conservation. Surprisingly, this did not happen. Instead, cosmologists exempted the big bang from energy conservation, but without saying how much was lost. This paper shows that, since t = 1 second after the big bang, expansion redshifting of CBR photons would have resulted in nonconservation-of-energy losses amounting to at least thirty million times the mass of the visible universe; moreover, losses continue at the rate of about a galactic mass every millennium. These results prove the big bang fails to match the physics of the real universe, that its expansion redshift hypothesis is fatally flawed, and hence that the big bang never possessed the qualifications necessary for being classified as a modern scientific theory. Disney has noted many uncertainties in big-bang cosmology [1], but he did not question whether its basic postulates agree with known conservation laws. This fourth paper does this, specifically focusing on whether spacetime
Give what is required and take only what you need! The effect of framing on rule-breaking in social dilemmas

To investigate the impact of framing on rule-breaking in social dilemmas, we incorporated a rule in a 1-shot resource game with 2 framing treatments: in one frame, we offered a give-some dilemma (i.e., a variant of a public goods game), and in the other frame, a take-some dilemma (i.e., a variant of a commons dilemma game). In each frame, all participants were part of 1 single collective sharing a common good. Each participant was initially equipped with 1 of 5 different endowments of points from which they must give/were allowed to take amounts to/from the common good. The rule established outcome equality between participants by prescribing the exact amounts of what to give/take to/from the common good, which was finally divided equally among participants. Participants decided whether to cooperate and comply with the rule or to break the rule to their own advantage and to the detriment of the collective (i.e., giving lower/taking higher amounts). The results of an online experiment with 202 participants showed a significantly higher proportion of individuals breaking the rule in the take-some dilemma than in the give-some dilemma. In addition, endowment size influenced the proportion of rule-breaking behavior in the take-some dilemma. However, the average amounts of points not given/taken too much were not different between the 2 dilemma types.
Case report of drug induce erythroderma in diabetic patient

Erythroderma, a severe form of skin reddening, is often difficult to diagnose and is usually caused by underlying inflammatory skin conditions. In this case report, we present the management of a patient diagnosed with drug-induced erythroderma. The patient developed generalized redness and scaling 21 days after receiving an unknown injection for pain from a local pharmacy. A thorough history and clinical examination were conducted, and drug-induced erythroderma was suspected. The patient was treated with a combination of mid-potency corticosteroids, liquid paraffin, recombinant human epidermal growth factor, and oral antihistamines. The patient recovered after strict diabetic diet control and was discharged
Awake Spine Surgery: Fad or Future?

Background data: Awake spine surgery has been an area of increasing interest, but it is still relatively uncommon. Purpose: The article aims to review the existing literature to summarize practices, outcomes, and trends in awake spine surgery to determine if awake spine surgery is merely a fad or the future of spine surgery. Study design: A narrative literature review. Patients and methods: The authors performed primary and secondary searches of the PubMed database to reveal works relevant to awake spine surgery. These results, in addition to works known to the authorship, were subjectively selected for inclusion in the narrative review based on relevance to the authors ’ aims. Results: Many types of spine surgery, from the lumbosacral to the cervical spine, can be performed in the awake patient. Anesthetic methods are varied and include, but are not limited to, spinal anesthesia, epidural anesthesia, and truncal blocks. These techniques may be used in isolation or combined. Patients that are ideal candidates for spine surgery have been well described, including patients receiving 1 e 2 level decompressions or fusion. Older patients may be good candidates for awake surgery. The outcomes associated with awake surgery are promising and seem superior to those associated with general anesthesia. There are multiple published protocols and instructions on selecting patients for and safely performing awake spine surgery. The incidence of awake spine surgery is increasing. Conclusion: Awake spine surgery is more than a fad and may be the future of spine surgery.
Discrepancy principle for generalized GN iterations combined with the reverse connection control

Abstract In this paper we investigate the generalized Gauss–Newton method in the following form x n+1 = ξn – θ(F′*(xn )F′(xn ), τn )F′*(xn ){(F(xn ) – ƒ δ ) – F′(xn )(xn – ξn )}, x 0, ξn ∈ 𝒟 ⊂ H 1. The modified source condition which depends on the current iteration point xn , is used. We call this inclusion the undetermined reverse connection. The new source condition leads to a much larger set of admissible control elements ξn as compared to the previously studied versions, where ξn = ξ. The process is combined with a novel a posteriori stopping rule, where is the number of the first transition of ‖F(xn ) – ƒ δ ‖ through the given level δω , 0, < ω < 1, i.e., The convergence analysis of the proposed algorithm is given.
Systematic triage and treatment of earthquake victims: Our experience in a tertiary hospital after the 2023 Kahramanmaras earthquake

Objectives The aim of this study was to evaluate the benefits of our triage system in acceleration of intervention for the musculoskeletal injuries and clinical follow-ups of trauma patients admitted to our center after the Kahramanmaras earthquake. Patients and methods Between February 6th, 2023 and February 20th, 2023, a total of 439 patients (207 males, 232 females; mean age: 37.1±19.1 years; range, 1 to 94 years) with earthquake-related musculoskeletal injuries after the Kahramanmaras earthquake were retrospectively analyzed. Data including age, sex, referral city information, removal time from the rubbles, physical examination findings, clinical photos, fasciotomy and amputation stumps and levels, and X-ray images and computed tomography images of all patients were shared and archived in the WhatsApp (Meta Platforms, Inc.® ATTN/CA, USA) group called ‘Earthquake’ created by orthopedic surgeons. To complete the patient interventions as soon as possible and to ensure order, the patients were distributed with the teams in order through this group by the consultant orthopedic surgeon. The treatments were applied and recorded according to the skin and soft tissue conditions, and fractures of the patients. All treatments were carried out with a multi-disciplinary approach. Results Of the patients, 16.2% were children. Lower limb injuries constituted 59.07% of musculoskeletal injuries. Upper limb, pelvic, and spinal cord injuries were observed in 21.9%, 12.7%, and 6.25%, respectively. Conservative treatment was applied to 183 (41.68%) patients. The most common surgical intervention was debridement (n=136, 53.1%). External fixation was applied in the first stage to 21 (8.2%) patients with open fractures. The mean removal time from the rubbles was 32.1±29.38 h. A total of 118 limb fasciotomy operations were applied to the patients. Fifty limb amputations were performed in 40 patients at the last follow-up due to vascular insufficiency and infection. Conclusion Based on our study results, we believe that a triage system using a good communication and organization strategy is beneficial to prevent treatment delay and possible adverse events in future disasters.
Kernel sections for processes and nonautonomous lattice systems

In this paper, we first establish a set of sufficient and necessaryconditions for the existence of globally attractive kernel sectionsfor processes defined on a general Banach space and a weighted spacel$_\rho ^p$ of infinite sequences ($p\geq 1)$, respectively.Then we obtain an upper bound of the Kolmogorov$\varepsilon$-entropy of kernel sections for processes on theHilbert space l$_\rho ^2 $. As applications, we investigatecompact kernel sections for first order, partly dissipative, andsecond order nonautonomous lattice systems on weighted spacescontaining bounded sequences.
Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape

We prove existence and uniqueness of classical solutions of the anisotropic prescribed mean curvature problem \begin{equation*} {\rm -div}\left({\nabla u}/{\sqrt{1 + |\nabla u|^2}}\right) = -au + {b}/{\sqrt{1 + |\nabla u|^2}}, \ \text{ in } B, \quad u=0, \ \text{ on } \partial B, \end{equation*} where $a,b>0$ are given parameters and $B$ is a ball in ${\mathbb R}^N$. The solution we find is positive, radially symmetric, radially decreasing and concave. This equation has been proposed as a model of the corneal shape in the recent papers [13,14,15,18,17], where however a linearized version of the equation has been investigated.