We study sheaves on holomorphic spaces of loops (also referred to as arcs ) and apply this to the study of the complex, defined in [2], governing deformations of the Poisson vertex algebra structure on the space of holomorphic loops into a Poisson variety. We describe this complex in terms of the (continuous) de Rham–Lie cohomology of an associated Lie algebroid object in locally linearly compact topological (alias Tate ) sheaves of modules on ℒ + M . In particular this allows us to easily compute the cohomology of the above in the case where π is symplectic, we obtain de Rham cohomology of M .

A bstract We compute squared matrix elements at next-to-next-to-leading order in perturbative quantum chromodynamics for the production of two or three (on- or off-shell) photons mediated via (light or heavy) quark loops. Our method handles all cases in a unified framework, using simultaneous subtraction of infrared, ultraviolet, and threshold singularities in loop momentum space to produce a locally finite integrand suitable for numerical integration. We confirm agreement with available analytic benchmarks at fixed phase-space points and provide new results otherwise. We also compute the double-virtual corrections to the cross section for on- and off-shell diphoton and on-shell triphoton production by combining the Monte Carlo integration over loop and phase space.

To compare and evaluate the clinical success of conventional, preformed, and three-dimensional (3D) printed band and loop (B and L) space maintainers. Forty-five participants in the age group of 5-7 years visiting the pediatric and preventive dentistry department, with grossly carious primary mandibular first molar of either side requiring extraction, were randomly divided into three groups: conventional, preformed, and 3D printed B and L space maintainer groups. Following extraction, the assigned space maintainer was fabricated and delivered. Clinical evaluation for survival and failure rates and gingival health was done at Baseline, 1, 3, 6, 9, and 12 months. Statistical analysis was performed using Chi-square or Fisher's exact tests, survival using Kaplan-Meier analysis, and ordinal data using Kruskal-Wallis and Mann-Whitney U tests. All space maintainers showed 100% survival at 1 and 3 months. At 12-months, conventional and preformed appliances demonstrated similar survival (86.7%), while the 3D printed group showed a lower rate (73.3%); however, differences were not statistically significant ( P > 0.05). Decementation was the primary cause of failure among all groups. Gingival and plaque scores increased over time in all groups. A significant difference in the gingival index was observed at 12 months ( P = 0.045), favoring the Preformed group. Plaque scores differed significantly at 9 and 12 months ( P < 0.05), with higher accumulation in the Conventional group. All three space maintainers demonstrated comparable 12-month survival; however, Preformed appliances showed relatively better gingival and plaque outcomes, with decementation identified as the predominant cause of failure across all groups.

Objectives: To evaluate and compare the acceptance, comfort, chairside time, and clinical outcomes of conventional and prefabricated band and loop space maintainers in children with premature loss of primary molars. Methods: Sixty children aged 4–8 years were randomly allocated into two groups: conventional band and loop space maintainer (CBLSM) and prefabricated band and loop space maintainer (PBLSM). Clinical procedures were performed by a single operator. Patient acceptance was evaluated after six months using a five-point Likert scale. Chairside time, space loss, gingival index, plaque index, and SEM (Sound, Eye, Motor) scale scores were recorded and statistically analyzed. Results: Both appliances showed comparable acceptance after six months with no statistically significant difference (p &gt; 0.05). Mild discomfort was reported by 40% in CBLSM and 46.6% in PBLSM groups. Mean chairside time was significantly lower in the conventional group (14.12 ± 3.90 minutes) compared to the prefabricated group (19.96 ± 5.55 minutes). Space loss was significant over six months, while gingival index differences were not statistically significant. Conclusions: Both conventional and prefabricated space maintainers demonstrated similar patient acceptance and comfort; however, conventional appliances required less chairside time.

This paper investigates critical points of the energy functional in sub-Finsler manifolds. Critical points of the energy functional correspond to sub-Finsler geodesics, i.e., horizontal curves that are extremal for the energy, emphasizing their importance in sub-Finsler geometry. Assuming that the sub-Finsler metric is bumpy (in the Morse–Bott sense), the energy functional on the free loop space has the Morse--Bott property, and we establish a direct link between critical points and closed geodesics. We shed light on the existence of at least one closed geodesic on compact sub-Finsler manifolds.

To evaluate and compare chairside clinical time and acceptance of prefabricated and conventional band and loop space maintainers in children with premature loss of primary molars. Sixty children aged 4-8 years with premature loss of primary first or second molars requiring a space maintainer were randomized into two groups: group 1, conventional band and loop space maintainer (CBLSM), and group 2, prefabricated band and loop space maintainer (PBLSM). The clinical evaluation for patient acceptance was carried out at six months follow-up using a five-point Likert scale. Patient comfort during clinical procedure, chairside clinical time, space loss, gingival index and plaque index were also recorded and compared between the two groups. After six months, both space maintainers were well accepted by the children, showing no statistically significant difference between the groups ( P > 0.05). In group 1, 40% of children, and in group 2, 46.6% of them showed mild discomfort measured using the Sound, Eye, Motor (SEM) scale, while the others were comfortable during the clinical procedure. The mean chairside clinical time required was 14.12 ± 3.90 and 19.96 ± 5.55 min for group 1 and group 2, respectively, and there was a statistically significant difference between the two groups ( P < 0.001). The plaque index, the gingival index and space loss after six months had no statistically significant differences between groups. The CBLSM and PBLSM were comparable in terms of patient acceptance, comfort during clinical procedure and space loss after six months. However, the mean chairside clinical time required was significantly higher in PBLSM group.

We compute the $\rm{SO}(n+1)$-equivariant mod $2$ Borel cohomology of the free iterated loop space $Z^{S^n}$ when $Z$ is a mod $2$ generalized Eilenberg Mac Lane space. When $n=1$, this recovers Bökstedt and Ottosen's computation for the free loop space. The highlight of our computation is a construction of cohomology classes using an $\mathrm{O}(n)$-equivariant evaluation map and a pushforward map.

Abstract In this note, we show that the Barutello–Ortega–Verzini regularization map is scale smooth.

Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension n n whose ( n − 1 ) (n-1) -skeleton is a co- H H -space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincaré Duality complex retracts off the loops of its ( n − 1 ) (n-1) -skeleton and describe its homology as a one-relator algebra.

Introduction: Oral health is crucial for young individuals’ overall well-being, yet disparities in utilization of dental services remain prevalent. Understanding the demographic factors influencing dental treatment patterns can help identify gaps in care and improve service delivery. Aims: This study analyzed the dental treatments received by pediatric patients at Taif University Dental Hospital and examined the relationship between patient demographics and dental procedures administered. Methods: In this retrospective cohort study, data were extracted from the dental records of patients aged 2–16 years, with a focus on various treatments, including prevention, restorations, pulp therapy, extractions, and interceptive orthodontics. Results and Discussion: This study included 791 cases that underwent 5287 dental procedures. Preventive treatments were most prevalent (35.1%), followed by restorations (28.8%), pulp treatments (13.5%), and extractions (12.9%). Children aged 8–10 and 11–13 years showed higher odds of receiving orthodontic appliances, while the 5–7 years of age group had increased odds of extraction, pulpotomy, and stainless steel crowns. Compared to females, males presented with reduced odds of receiving braces (odds ratio [OR] = 0.250) and strip crowns (OR = 0.694) but increased odds of undergoing pulp treatments (OR = 2.214), scaling (OR = 2.037), stainless steel crown placement (OR = 2.412), and extractions (OR = 1.429). Compared to Black individuals, White individuals had higher odds of receiving braces (OR = 9.512) and band and loop space maintainers (OR = 5.198). Both White and Asian individuals were significantly more likely to undergo extractions, pulpectomies, and pulpotomies. Saudis exhibited higher odds for receiving braces (OR = 6.500) compared to non-Saudis. Conversely, Saudis had lower odds of receiving extractions (OR = 0.786) and scaling (OR = 0.733). Conclusion: This study reveals significant disparities in dental service utilization among young patients at Taif University Dental Hospital, with age, gender, race, and nationality profoundly influencing the patterns of treatment received.

This paper presents the design of simple, robust, and efficient shunt active power filter (SAPF) using a loop in loop (cascaded) PI controller and Space vector pulse width modulated synchronous reference frame (dq) controller to mitigate harmonics from a three-phase diode rectifier (nonlinear load) catering to variety of loads (R, and R-L), supplied by a microgrid (week grid) having plethora of distributed generator, exhibiting heuristic nature. The intermittent nature of DGs leads to variation in voltage and frequency, and load variation aggravates this situation further. Placement and availability of DGs in the microgrid lead to the variation in cable length, causing variation in the reactance presented between the source and the point of common coupling, where a SAPF is deployed. A robust control mechanism of SAPF has been presented here that gives compliance to IEEE-519 amidst the mentioned perturbations in voltage, frequency, and grid reactance using a passively damped LCL filter and a smaller DC-bus capacitor due to the presence of SVPWM control. A constant frequency switched Space Vector Pulse Width Modulation (SVPWM) control makes the SAPF simpler and more reliable. Further, a cascaded PI controller, one controlling DC-bus voltage and another controlling the filter’s current, makes it more efficient and reliable. Simulation and comparative analytical results of SVPWM with that of Sinusoidal PWM (SPWM) validate the design’s suitability for enhancing power quality in the given system.

BackgroundThe aim of this study was to evaluate the effect of band and loop space maintainers, fabricated using digital technologies, and the luting cements used for their fixation, on mesio-distal tooth movement using the Finite Element Analysis method. Additionally, the biomechanical performance of the materials was analyzed by comparing the maximum Von Mises stress distribution. Methodology: A total of fifteen finite element models were created using combinations of five different band and loop materials (BruxZir, Conventional, Trilor, polyetheretherketone and carbon fiber-reinforced polyetheretherketone) and three types of luting cements: conventional glass ionomer cement, resin-modified glass ionomer cement, and dual-cure resin cement. A vertical force of 70 Newton was applied in the occluso-gingival direction at the band-loop junction in each model. Stress distribution and potential failure zones were analyzed using the finite element analysis method. Results: Among the tested materials, BruxZir exhibited the least amount of displacement and generated the lowest stress on the tooth. It was followed by Conventional, Trilor, and carbon fiber-reinforced polyetheretherketone and polyetheretherketone. Polyetheretherketone showed the highest level of displacement. When comparing luting cements, the resin-modified glass ionomer, which has the lowest elastic modulus, caused the greatest mesial movement. This was followed by the self-adhesive resin cement and the conventional glass ionomer cement. Conclusions: The integration of digital technologies in pediatric dentistry enables the clinical use of space maintainers fabricated from various advanced materials. However, further clinical studies are necessary to assess the long-term success and biocompatibility of these digital materials.

Background: In paediatric dentistry, space maintainer is crucial for maintaining arch length after early tooth loss. Dental arch development can be greatly impacted by the early loss of primary teeth, particularly posterior teeth like primary molars. Adjacent teeth may drift, the midline may deviate, the length of the arch may shorten, and the emergence of permanent successors may be disrupted. Purpose: The goal of this case study is to demonstrate how well a prefabricated space maintainer works for a young child who needs few dental appointments. Case: The lower right primary first molar of a 5-year-old kid had significant caries. With neighbouring teeth intact and no indications of infection or systemic anomalies, a clinical and radiographic evaluation confirmed the need for extraction. Case Management: Tooth #84 was extracted under local anaesthesia the same day, and a prefabricated band and loop space maintainer was chosen. Without the need for laboratory procedures, the appliance was modified chairside and cemented in a single visit. For the underlying permanent successor, it offered appropriate space maintenance. To evaluate oral hygiene and appliance stability, the patient was scheduled for routine follow-ups. This case demonstrates the clinical advantage of utilising a premade band and loop space maintainer in a single-visit procedure after a young child's non-restorable primary molars were extracted. Conclusion: When cooperation or access to care is restricted, preformed space maintainers provide a rapid, efficient, and kid-friendly way to preserve arch integrity after early tooth loss in the primary dentition.

Abstract We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincaré duality theorem between homology and cohomology that preserves this structure. This lifts to a duality theorem between graded open–closed topological quantum field theories (TQFTs). We use in a systematic way the formalism of Tate vector spaces. Specializing to the case of cotangent bundles, we define Rabinowitz loop homology and cohomology and explain from a unified perspective pairs of dual results that have been observed over the years in the context of the search for closed geodesics. These concern critical levels, relations to the based loop space, manifolds all of whose geodesics are closed, Bott index iteration, and level potency. Moreover, the graded Frobenius algebra structure gives meaning and proof to a relation conjectured by Sullivan between the loop product and coproduct.

In this paper, we consider the Chas-Sullivan loop space homology H*(XS1) of a formal elliptic 2-stage Postnikov tower X. We show that the center of the graded Lie algebra sH*(XS1; Q) on a minimal Sullivan model of X is non-trivial.

Introduction:Primary teeth serve as the best space maintainer for permanent dentition. However, in cases with premature loss of primary teeth, the best way to prevent future malocclusion would be to place an effective space maintainer.Aim:This study aimed to evaluate the clinical performance of intraorally scanned and direct metal laser sintered (DMLS) band and loop space maintainers in terms of survival rate, gingival health, and patient satisfaction.Materials and Methodology:In this pilot study, 10 children aged between 4 and 9 years who met the inclusion criteria were selected. Intraoral scanning was performed, and a 3D cast was printed, on which a band and loop space maintainer was fabricated. The printed band and loop were cemented and evaluated at 1, 3, and 6 months. Patient satisfaction was assessed at baseline. Data were subjected to statistical analysis using the Friedman test.Result:The survival rate showed a statistically significant improvement over time, with mean scores increasing from 1.20 at baseline to 2.0 at 6 months (P = 0.001). Gingival inflammation progressively increased from a score of 1.0-2.0 over time, showing a statistically significant difference (P = 0.049). Patient satisfaction at baseline was generally high.Conclusion:The findings highlight 3D printing as a promising advancement in pediatric dentistry, combining superior performance with enhanced patient satisfaction.

The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and by Ziller to study the string topology coproduct and the Chas-Sullivan product on compact symmetric spaces. We show that the Chas-Sullivan product for compact symmetric spaces is highly non-trivial for any rank and we prove that there are many non-nilpotent classes whose powers correspond to the iteration of closed geodesics. Moreover, we show that the based string topology coproduct is trivial for compact symmetric spaces of higher rank and we study the implications of this result for the string topology coproduct on the free loop space.

Abstract We provide a homotopy equivalence for the loop space of the polyhedral product associated with a simplicial complex formed via the polyhedral join operation, and give sufficient conditions under which this loop space is a finite-type product of spheres and loops on spheres.

A bstract We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3 + 1)-dimensional Minkowski space-time, possess exact structures that resemble integrability, with an infinite number of conserved charges in involution. Such structures live in the space of non-abelian electric and magnetic charges, and are based on flat connections in generalized loop spaces, presenting an R -matrix, and Sklyanin relation. We present two novel symmetries of Yang-Mills theories. The first one corresponds to global transformations generated by the infinity of those conserved charges under the Poisson brackets. The gauge and matter fields, as well as Wilson lines and fluxes, have interesting transformation laws under such a global symmetry. The second one corresponds to symmetries of the integral Yang-Mills equations, which lead to the conserved charges. They generate an infinite-dimensional group, where the elements are holonomies of connections on the loop space of functions from the circle S 1 to the space-time. Our approach certainly applies to the Standard Model of the Fundamental Interactions. The conserved charges are gauge invariant, and so, in the case of QCD, they are color singlets and perhaps are not confined. Therefore, the hadrons may carry such charges. Our results open up the way for the construction of non-perturbative methods for Yang-Mills theories.

We correct here two errors in our earlier paper An algebraic model for finite loop spaces. 55R35; 20D20, 20E22We correct two erroneous arguments found in [3].In the proof of [3, Lemma A.8], we applied [2, Proposition 5.4] to orbit categories of transporter systems, while that proposition is stated only for orbit categories of fusion systems.After replacing that by Proposition 2.3 below, Lemma A.8 can be proven as stated in [3].In the proof of [3, Corollary A.10], we applied [3, Proposition A.9(b)] in a way that is not valid unless all objects in L are F-centric.That corollary is a special case of Proposition 1.6 here. Inclusions of linking systems for the same fusion systemWe refer to [3, Definition 1.9] for the complete definition of a linking system associated to a fusion system F over a discrete p-toral group S .Very briefly, it consists of a category L whose objects are subgroups of S, together with a pair of functors T Ob.L/ .