Proof of the universal density of charged states in QFT

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

Thermal correlation functions in CFT and factorization

We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in d dimensions in terms of the c-anomaly coefficient. By including α′ corrections to the black brane background, we reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula. When the dimensions satisfy ∆i = ∆j + ∆k, the thermal 3-point function satisfies a factorization property. We argue that in d > 2 factorization is a reflection of the semiclassical regime.

Use of various keratometry data (ring and zone) in trifocal IOL calculation

Purpose. To compare the results of trifocal IOL calculation using various corneal tomographic data (ring and zone). Methods. This retrospective study involved 46 patients (46 eyes), underwent cataract surgery with trifocal IOL implantation (AcrySof IQ PanOptix). The calculation was performed using Tomey OA-2000 according to 2 formulas (Barrett II Universal, Olsen). Keratometry values included Km (the average of two main meridians of a cornea) provided by Pentacam HR Power Distribution Apex map, which describes total corneal refractive power (TCRP) with diameter of 3.0, 4.0 and 5.0 mm on a ring and zone. Mean (MAE) and median (MedAE) predicted postoperative refraction errors were assessed after surgery. Results. Mean Km value on 3 mm zone and ring was: 42.75±1,46 D and 42,91±1,43 D, respectively (p<0,0001). Mean Km on 4 mm zone and ring was: 42.6±1.5 D and 43.3 ± 1.5 D, respectively (p <0.005). Mean Km value on 5 mm zone and ring was: 43,09±1,5 D and 43,55±1,48 D, respectively (p<0,0001). Calculations using the Barrett II Universal formula revealed significant difference between MAE and MedAE of the predicted postoperative refraction on 5mm zone and ring (p=0.045). When using the Olsen formula in the calculations, significant difference was revealed using the Km data with a diameter of 3 mm and 5 mm (p=0.001 и p=0.009, respectively). The calculation on 3 mm ring was more accurate than for 3 mm zone. With a 5 mm diameter, the calculation is more accurate according to the zone data. Conclusion. Mean Km value on Power Distribution Apex map according to ring is significantly greater then according to zone. 1) The calculation of the trifocal IOL based on the TCRP zone data is reliably more accurate than the ring data according to both formulas (Barrett II Universal and Olsen) with a diameter of 5 mm. 2) According to the Olsen formula with a diameter of 3 mm, the calculation of the optical power of trifocal IOL based on TCRP ring data is more accurate. Key words: IOL calculation, Trifocal IOL, corneal topography

Algorithm for constructing a route to pass a narrow fairway

Modern navigation systems often employ the algorithms for plotting lines for the preliminary route construction. The current conditions of technological development imply the simplicity of constructing routes. However, the most important part was and remains the speed of the system that generates the route. The authors of the paper proposed a universal algorithm for constructing a navigation route in narrow channels of the sea. The presented algorithm identifies the middle of the fairway as the safest point at each narrow segment and connects them with track lines. The problem that can arise is smoothing, as the middle of the fairway can shift significantly. To solve this problem, new relative and absolute parameters that characterize plotting of turning points were introduced. In addition, a unified universal formula was proposed for finding the coordinates of these points on a line perpendicular to the current route of the vessel. It was experimentally proved that correctly selected empirical parameters enable the algorithm to quickly construct a route in any navigation area with a relatively low computational complexity. This approach is appropriate for clearly delineated zones of the fairway, and it is compatible with zone methods.

Duality relations for overlaps of integrable boundary states in AdS/dCFT

The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a universal formula in the case of overlaps between Bethe eigenstates and integrable boundary states, of relevance for AdS/dCFT, by determining the transformation properties of the overlaps under fermionic as well as bosonic dualities which allows us to move between any two descriptions of the spin chain encoded in the QQ-system. An important part of our analysis involves introducing a suitable regularization for singular Bethe root configurations.

ABLATIVE PRESSURE PULSE

<div> We examine herein a simple model for the evolution in time of the pressure which a suddenly vaporized, ablating layer exerts upon the subjacent body. The model invokes a plausible construct of surface material instantaneously thrust into a gaseous regime governed by a Maxwell-Boltzmann phase space distribution. The surface pressure <i>per se</i> is gotten by computing the time rate of change of the momentum per unit area which the retrograde molecules, and only those, transfer through impact/reflection to the unvaporized body below. An explicit pressure formula, one alluding to the variable gas temperature within the vaporized layer, is obtained as a single quadrature requiring numerical integra- tion at finite times past the onset of impact. Limiting, null pressure values, both close-in and in pulse aftermath, can nevertheless be extracted in analytic terms, confirming in particular the indispensable asymptotic evanescence. A universal formula in dimensionless variables is given for pressure versus time, both suitably normalized.</div>

ABLATIVE PRESSURE PULSE

<div> We examine herein a simple model for the evolution in time of the pressure which a suddenly vaporized, ablating layer exerts upon the subjacent body. The model invokes a plausible construct of surface material instantaneously thrust into a gaseous regime governed by a Maxwell-Boltzmann phase space distribution. The surface pressure <i>per se</i> is gotten by computing the time rate of change of the momentum per unit area which the retrograde molecules, and only those, transfer through impact/reflection to the unvaporized body below. An explicit pressure formula, one alluding to the variable gas temperature within the vaporized layer, is obtained as a single quadrature requiring numerical integra- tion at finite times past the onset of impact. Limiting, null pressure values, both close-in and in pulse aftermath, can nevertheless be extracted in analytic terms, confirming in particular the indispensable asymptotic evanescence. A universal formula in dimensionless variables is given for pressure versus time, both suitably normalized.</div>

Expanding on the Cardy-like limit of the SCI of 4d $$ \mathcal{N} $$ = 1 ABCD SCFTs

We study the Cardy-like limit of the superconformal index of generic $$ \mathcal{N} $$ N = 1 SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugacities associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. We corroborate the validity of our proposal by studying several examples, beyond the well-understood toric class. We compute the index also for models without a weakly-coupled gravity dual, whose gravitational anomaly is not of order one.

Does Every Calculation Formula Fit for All Types of Intraocular Lenses? Optimization of Constants for Tecnis ZA9003 and ZCB00 Is Necessary

Background and Objectives: To evaluate the performance of intraocular lenses (IOLs) using power calculation formulas on different types of IOL. Materials and Methods: 120 eyes and four IOL types (BioLine Yellow Accurate Aspheric IOL (i-Medical), TECNIS ZCB00, TECNIS ZA9003 (Johnson & Johnson) (3-piece IOL) and Softec HD (Lenstec)) were analyzed. The performance of Haigis, Barret Universal II and SKR-II formulas were compared between IOL types. The mean prediction error (ME) and mean absolute prediction error (MAE) were analyzed. Results: The overall percentage of eyes predicted within ±0.25 diopters (D) was 40.8% for Barret; 39.2% Haigis and 31.7% for SRK-II. Barret and Haigis had a significantly lower MAE than SRK-II (p < 0.05). The results differed among IOL types. The largest portion of eyes predicted within ±0.25 D was with the Barret formula in ZCB00 (33.3%) and ZA9003 (43.3%). Haigis was the most accurate in Softec HD (50%) and SRK-II in Biolline Yellow IOL (50%). ZCB00 showed a clinically significant hypermetropic ME compared to other IOLs. Conclusions: In general, Barret formulas had the best performance as a universal formula. However, the formula should be chosen according to the type of IOL in order to obtain the best results. Constant optimizations are necessary for the Tecnis IOL ZCB00 and ZA9003, as all of the analyzed formulas achieved a clinically significant poor performance in this type of IOL. ZCB00 also showed a hypermetropic shift in ME in all the formulas.