A Further Extension of the KKMS Theorem

Recently Reny and Wooders ([23]) showed that there is some point in the intersection of sets in Shapley's ([24]) generalization of the Knaster-Kuratowski-Mazurkiwicz Theorem with the property that the collection of all sets containing that point is partnered as well as balanced. In this paper we provide a further extension by showing that the collection of all such sets can be chosen to be strictly balanced, implying the Reny-Wooders result. Our proof is topological, based on the Eilenberg-Montgomery fixed point Theorem. Reny and Wooders ([23]) also show that if the collection of partnered points in the intersection is countable, then at least one of them is minimally partnered. Applying degree theory for correspondences, we show that if this collection is only assumed to be zero dimensional (or if the set of partnered and strictly balanced points is of dimension zero), then there is at least one strictly balanced and minimally partnered point in the intersection. The approach presented in this paper sheds a new geometric-topological light on the Reny-Wooders results.

Extensions of some differential inequalities for fractional integro-differential equations via upper and lower solutions

This paper deals with some differential inequalities for generalized fractional integro-differential equations by using the technique of upper and lower solutions. The fractional differential operator is taken in Caputo’s sense and the nonlinear term divided into two parts depends on the fractional integrals of an unknown function with two different fractional orders. The results are studied by employing a variety of coupled upper and lower solutions. These theorems have some potential for extending the iterative techniques to fractional order integro-differential equations and to coupled systems of integro-differential fractional equations to obtain the existence of solutions as well as approximate solutions for the considered problem

New Stratigraphic and Palaeogeographic Results from the Palaeozoic and Early Mesozoic of the Middle Pontides (Northern Turkey) in the Azdavay, Devrekani, Küre and Inebolu Areas: Implications for the Carboniferous-Early Cretaceous Geodynamic Evolution and Some Related Remarks to the Karakaya Oceanic Rift Basin

The Küre Complex of the Middle Pontides, northern Turkey, is not a remnant of the Palaeotethys but consists of three different units with differing geological history, the Küre Ridge Unit, the Küre Ocean Unit and the Çalça Unit. The Küre Ridge Unit consists of the Serveçay Group, a pre-Permian, low-grade metamorphic Variscan oceanic sequence, and the Sirçalik Group, a Lower and Middle Triassic shallow-water sequence of North Alpine facies and event succession which disconformably overlies the Serveçay Group. Following a hiatus, the Sirçalik Group is overlain by marginal parts of the Akgöl Group with olistoliths of local origin which were derived mainly from the Sirçalik Group. The Küre Ocean Unit consists mostly of the Akgöl Group (siliciclastic turbidites and olistostromes of the Karadagtepe Formation, which is a middle Carnian to Middle Jurassic accretionary complex from the southern, active margin of the Küre Ocean, and mainly Middle Jurassic molasse type shallow-water sandstones, siltstones and shales of an unnamed formation) and of thick oceanic basalts (Ipsinler Basalt). Tectonic slices of Middle Triassic to lower Carnian ophiolites and basalts are also present. The Karadagtepe Formation contains numerous Middle Triassic exotic olistoliths and blocks of shallow-water and predominantly slope and basinal limestones, ocean-floor deep-sea sediments (shales and radiolarites), basalts and small clasts of ophiolites or ophiolitic detritus. The Çalça Unit consists of deposits from the northern, passive margin of the Küre ocean with many Pelsonian to upper Norian Hallstatt Limestones and Rhaetian-Lower Jurassic (?Middle Jurassic) deep-water shales and marls. All three units are overlain following a period of non deposition by the Upper Jurassic Bürnük Formation (red conglomerate, sandstone) and Inalti Formation (shallow-water platform carbonates). The Küre Ridge Unit was split away from the Variscan Sakarya Continent by the opening of the Karakaya oceanic rift basin during latest Permian (Dorashamian) and became a continental splinter between the Karakaya oceanic rift basin and the Küre Ocean (opened during the late Scythian). Southward subduction began in the Küre Ocean during the middle Carnian (beginning of the Karadagtepe siliciclastic turbidites), whereas at the northern passive margin the deposition of Hallstatt Limestones continued until the latest Norian. The deposition of siliciclastic turbidites and olistostromes (Diskaya Unit) began in the entire Karakaya oceanic rift basin during the middle Carnian, and ocean basin deposits (radiolarites, pelagic limestones) and slope deposits form the passive margin (e.g., Hallstatt Limestones) are no more present in the Karakaya oceanic rift basin indicating that this basin was very narrow (only a few hundreds of kilometres). During the late Norian, the Karakaya oceanic rift basin closed, whereas subduction at the southern (active margin) of the Küre ocean continued. At the northern margin of the (Upper Triassic?) Jurassic-Lower Cretaceous Beykoz-Çaglayan turbidite basin (north of the Küre Complex) the accretionary complex of an older ocean, the Late Palaeozoic Paphlagonian Ocean, was exposed that yielded clasts in the Beykoz-Çaglayan turbidite basin. Among these clasts Carboniferous to Middle Permian (Capitanian) pelagic rocks (pelagic limestones, radiolarites) could be dated. A Middle to Late Permian southward-directed subduction is assumed for the Paphlagonian Ocean. Its closure occurred either at the end of the Permian or during the Scythian

Serum IGF-1 Affects Skeletal Acquisition in a Temporal and Compartment-Specific Manner

Insulin-like growth factor-1 (IGF-1) plays a critical role in the development of the growing skeleton by establishing both longitudinal and transverse bone accrual. IGF-1 has also been implicated in the maintenance of bone mass during late adulthood and aging, as decreases in serum IGF-1 levels appear to correlate with decreases in bone mineral density (BMD). Although informative, mouse models to date have been unable to separate the temporal effects of IGF-1 depletion on skeletal development. To address this problem, we performed a skeletal characterization of the inducible LID mouse (iLID), in which serum IGF-1 levels are depleted at selected ages. We found that depletion of serum IGF-1 in male iLID mice prior to adulthood (4 weeks) decreased trabecular bone architecture and significantly reduced transverse cortical bone properties (Ct.Ar, Ct.Th) by 16 weeks (adulthood). Likewise, depletion of serum IGF-1 in iLID males at 8 weeks of age, resulted in significantly reduced transverse cortical bone properties (Ct.Ar, Ct.Th) by 32 weeks (late adulthood), but had no effect on trabecular bone architecture. In contrast, depletion of serum IGF-1 after peak bone acquisition (at 16 weeks) resulted in enhancement of trabecular bone architecture, but no significant changes in cortical bone properties by 32 weeks as compared to controls. These results indicate that while serum IGF-1 is essential for bone accrual during the postnatal growth phase, depletion of IGF-1 after peak bone acquisition (16 weeks) is compartment-specific and does not have a detrimental effect on cortical bone mass in the older adult mouse

MRI after Whoops procedure:diagnostic value for residual sarcoma and predictive value for an incomplete second resection

OBJECTIVE: To determine the value of MRI for the detection and assessment of the anatomic extent of residual sarcoma after a Whoops procedure (unplanned sarcoma resection) and its utility for the prediction of an incomplete second resection. MATERIALS AND METHODS: This study included consecutive patients who underwent a Whoops procedure, successively followed by gadolinium chelate-enhanced MRI and second surgery at a tertiary care sarcoma center. RESULTS: Twenty-six patients were included, of whom 19 with residual tumor at the second surgery and 8 with an incomplete second resection (R1: n = 6 and R2: n = 2). Interobserver agreement for residual tumor at MRI after a Whoops procedure was perfect (κ value: 1.000). MRI achieved a sensitivity of 47.4% (9/19), a specificity of 100% (7/7), a positive predictive value of 100% (9/9), and a negative predictive value of 70.0% (7/17) for the detection of residual tumor. MRI correctly classified 2 of 19 residual sarcomas as deep-seated (i.e., extending beyond the superficial muscle fascia) but failed to correctly classify 3 of 19 residual sarcomas as deep-seated. There were no significant associations between MRI findings (presence of residual tumor, maximum tumor diameter, anatomic tumor extent, tumor margins, tumor spiculae, and tumor tail on the superficial fascia) with an incomplete (R1 or R2) second resection. CONCLUSION: Gadolinium chelate-enhanced MRI is a reproducible method to rule in residual sarcoma, but it is insufficiently accurate to rule out and assess the anatomic extent or residual sarcoma after a Whoops procedure. Furthermore, MRI has no utility in predicting an incomplete second resection

Predictive value of a false-negative focused abdominal sonography for trauma (FAST) result in patients with confirmed traumatic abdominal injury

OBJECTIVE: To investigate if patients with confirmed traumatic abdominal injury and a false-negative focused abdominal sonography for trauma (FAST) examination have a more favorable prognosis than those with a true-positive FAST. METHODS: This study included 97 consecutive patients with confirmed traumatic abdominal injury (based on computed tomography [CT] and/or surgical findings) who underwent FAST. RESULTS: FAST was false-negative in 40 patients (41.2%) and true-positive in 57 patients (58.8%). Twenty-two patients (22.7%) had an unfavorable outcome (defined as the need for an interventional radiologic procedure, laparotomy, or death due to abdominal injury). Univariately, a false-negative FAST (odds ratio [OR] 0.24; p = 0.017) and a higher systolic blood pressure (OR, 0.97 per mmHg increase; p = 0.034) were significantly associated with a favorable outcome, whereas contrast extravasation on CT (OR, 7.17; p = 0.001) and shock index classification (OR, 1.89 for each higher class; p = 0.046) were significantly associated with an unfavorable outcome. Multivariately, only contrast extravasation on CT remained significantly associated with an unfavorable outcome (OR, 4.64; p = 0.016). When excluding contrast extravasation on CT from multivariate analysis, only a false-negative FAST result was predictive of a favorable outcome (OR, 0.28; p = 0.038). CONCLUSION: Trauma patients with confirmed abdominal injury and a false-negative FAST have a better outcome than those with a positive FAST. FAST may be valuable for risk stratification and prognostication in patients with a high suspicion of abdominal injury when CT has not been performed yet or when CT is not available

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

Clinical implications of increased uptake in bone marrow and spleen on FDG-PET in patients with bacteremia

PURPOSE: To investigate which clinical factors and laboratory values are associated with high FDG uptake in the bone marrow and spleen on 2-deoxy-2-[18F]fluoro-D-glucose (FDG) positron emission tomography (PET)/computed tomography (CT) in patients with bacteremia.METHODS: One hundred forty-five consecutive retrospective patients with bacteremia who underwent FDG-PET/CT between 2010 and 2017 were included. Mean standard uptake values (SUVmean) of FDG in bone marrow, liver, and spleen were measured. Bone marrow-to-liver SUV ratios (BLR) and spleen-to-liver SUV ratios (SLR) were calculated. Linear regression analyses were performed to examine the association of BLR and SLR with age, gender, hemoglobin, leukocyte count, platelets, glucose level, C-reactive protein (CRP), microorganism, days of antibiotic treatment before FDG-PET/CT, infection focus, use of immunosuppressive drugs, duration of hospital stay (after FDG-PET/CT), ICU admission, and mortality.RESULTS: C-reactive protein (p = 0.006), a cardiovascular or musculoskeletal focus of infection (p = 0.000 for both), and bacteremia caused by Gram-negative bacteria (p = 0.002) were independently and positively associated with BLR, while age (p = 0.000) and glucose level before FDG-PET/CT (p = 0.004) were independently and negatively associated with BLR. For SLR, CRP (p = 0.001) and a cardiovascular focus of infection (p = 0.020) were independently and positively associated with SLR, while age (p = 0.002) and glucose level before FDG-PET/CT (p = 0.016) were independently and negatively associated with SLR.CONCLUSION: High FDG uptake in the bone marrow is associated with a higher inflammatory response and younger age in patients with bacteremia. In patients with high FDG uptake in the bone marrow, a cardiovascular or musculoskeletal focus of infection is more likely than other foci, and the infection is more often caused by Gram-negative species. High splenic FDG uptake is associated with a higher inflammatory response as well, and a cardiovascular focus of infection is also more likely in case of high splenic FDG uptake.</p

Design and Characterization of a Hypervelocity Expansion Tube Facility

We report on the design and characterization of a 152 mm diameter expansion tube capable of accessing a range of high enthalpy test conditions with Mach numbers up to 7.1 for aerodynamic studies. Expansion tubes have the potential to offer a wide range of test flow conditions as gas acceleration is achieved through interaction with an unsteady expansion wave rather than expansion through a fixed area ratio nozzle. However, the range of test flow conditions is in practice limited by a number of considerations such as short test time and large amplitude flow disturbances. We present a generalized design strategy for small-scale expansion tubes. As a starting point, ideal gas dynamic calculations for optimal facility design to maximize test time at a given Mach number test condition are presented, together with a correction for the expansion head reflection through a non-simple region. A compilation of practical limitations that have been identified for expansion tube facilities such as diaphragm rupture and flow disturbance minimization is then used to map out a functional design parameter space. Experimentally, a range of test conditions have been verified through pitot pressure measurements and analysis of schlieren images of flow over simple geometries. To date there has been good agreement between theoretical and experimental results