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Let ?A and ?B be two homomorphisms on Banach algebras A and B, respectively. In this paper, we study ?-amenability, ?-weak amenability, ?-biflatness, and ?-biprojectivity of triangular Banach algebras of the form T?A,?B, where ? = ?A ? ?B.

We define and study approximate versions of σ-biflatness and σ-biprojectivity of a Banach algebra A where σ ∈Hom(A). We generalize the concepts pseudo amenability and pseudo contractibility via homomorphisms. We investigate their relations.

Generalising the concept of injectivity, we study the notion of $\varphi $ -injectivity for dual Banach algebras. It provides a framework for studying $\varphi $ -amenability of enveloping dual Banach algebras.

An improved design for the uniform substrate integrated waveguide (SIW) long slot leaky wave antenna (LWA) is presented in this communication. To achieve the desired sidelobe level (SLL), beamwidth and beam direction, proper distributions for leakage constant and phase constant should be created along the slot. An accurate calculation of leakage and phase constants is performed by considering an unwanted mode, in addition to the leaky mode, along the uniform LWA structure. Considering this unwanted mode in the design procedure results in good consistency between the desired and designed radiation patterns. The presented LWA realizes a Taylor distribution with predefined SLL of −25 dB at 17 GHz. The radiation pattern, amplitude distribution, and phase distribution of the designed antenna are compared with the desired ones. This comparison shows the high accuracy of the proposed design procedure. Measurement results are also presented at 16.5, 17, and 17.5 GHz for validation of the design procedure.

Even though the prevalence of VSR after MI is only 1%-3%, the mortality associated with the condition is more than 80%. Very few studies in the literature have described in detail the treatment options for delayed VSR repair. This systematic review was conducted to evaluate the outcomes of delayed ventricular septal rupture (VSR) repair following acute myocardial infarction (AMI). Digital databases were searched systematically to identify studies reporting the outcomes of delayed VSR repair. Detailed study and patient-level baseline characteristics including the type of study, sample size, follow-up, number of delayed repairs, time to repair, outcomes (in terms of major adverse cardiovascular events), and predictors of outcome were abstracted. A total of 12 studies, recruiting 8,579 patients were included in the final analysis. Male gender, young age (60 years), and delayed VSR repair were reported as predictors of survival along with left ventricular assist devices (LVADs) and extracorporeal membrane oxygenation (ECMO), and the use of inotropes before surgery. Postoperative renal failure, higher New York Heart Association (NYHA) score, early repair, and history of heart failure (HF) were demonstrated as predictors of mortality. This study demonstrated that delayed VSR repair can reduce mortality in patients who develop VSR after AMI. Furthermore, the use of LVADs can prolong the time of surgery, and the use of inotropes can predict survival benefits in this patient cohort.

We introduce a new concept of $$\sigma$$-biflatness for Banach algebras. We show difference between this new concept and the classical one. A characterization of $$\sigma$$-biflatness is also given. As we shall see, $$\sigma$$-biflatness is closely related to the notions of $$\sigma$$-amenability and $$\sigma$$-biprojectivity. We compare our definition with the existing notion of $$\sigma$$-biflat Banach algebras in the sense of Ghorbani and Bami (Bull Iran Math Soc 39(3):507–515, 2013). In addition, $$\sigma$$-biflatness of tensor product of Banach algebras is discussed.

Bacterial cellulose (BC) is an extracellular natural polymer produced by many microorganisms and its properties could be tailored via specific fabrication methods and culture conditions. There is a...

We show that an essentially amenable Banach algebra need not have an approximate identity. This answers a question posed by Ghahramani and Loy [‘Generalized notions of amenability’, J. Funct. Anal. 208 (2004), 229–260]. Essentially Connes-amenable dual Banach algebras are introduced and studied.

We find some relations between module biprojectivity and module biflatness of Banach algebras $\mathcal A$ and $\mathcal B$ and their projective tensor product $\mathcal A \mathbin{\widehatøtimes}\mathcal B$. For some semigroups $S$, we study module biprojectivity and module biflatness of semigroup algebras $l^1(S)$.

The momentous objective in this paper is to prove existence as well as approximations of solution in hybrid initial value problem with fractional q-derivative in Caputo sense. The main approach is based on the operator theoretic technique in a partially ordered metric space. The results are obtained under weaker partially conditions and partially Lipschitz conditions via Dhage iteration method. Examples illustrating the results are also presented.

This study presents a new design for the substrate integrated waveguide (SIW) long slot leaky wave antenna (LWA) with narrow beam, low side lobe level (SLL) and low cross-polarisation. To meet these specifications, the changes of phase constant, β, along the structure are compensated, the required leakage constant, α r , is determined more accurately by considering the loss and a straight slot along the antenna is used. In order to calculate the leakage constant of the leaky-mode more accurately, thru-reflect-line method along with HFSS simulations is used. By properly determining the shape of SIW walls, the amount of leakage along the slot and the phase constant can be controlled. This results in a desired aperture amplitude and phase distribution. The presented LWA realises a Taylor distribution with a predefined SLL of -25 dB. Such a design also leads to a low cross-polarisation level and narrow beam at centre frequency of 17 GHz. The measurement results are consistent with the simulation results.

The present study was designed to characterize transduction of non-human primate brain and spinal cord with a modified adeno-associated virus serotype 2, incapable of binding to theheparan sulfate proteoglycan receptor, referred to as AAV2-HBKO. AAV2-HBKO was infused into the thalamus, intracerebroventricularly or via a combination of both intracerebroventricular and thalamic delivery. Thalamic injection of this modified vector encoding GFP resulted in widespread CNS transduction that included neurons in deep cortical layers, deep cerebellar nuclei, several subcortical regions, and motor neuron transduction in the spinal cord indicative of robust bidirectional axonal transport. Intracerebroventricular delivery similarly resulted in widespread cortical transduction, with one striking distinction that oligodendrocytes within superficial layers of the cortex were the primary cell type transduced. Robust motor neuron transduction was also observed in all levels of the spinal cord. The combination of thalamic and intracerebroventricular delivery resulted in transduction of oligodendrocytes in superficial cortical layers and neurons in deeper cortical layers. Several subcortical regions were also transduced. Our data demonstrate that AAV2-HBKO is a powerful vector for the potential treatment of a wide number of neurological disorders, and highlight that delivery route can significantly impact cellular tropism and pattern of CNS transduction.

It is shown that various definitions of $��$-Connes amenability as introduced independently in \cite{Gh-Ja, mah, Sh-Am}, are just rediscovering existing notions and presenting them in different ways. It is also proved that even $��$-contractibility as defined in \cite{Sangani}, is equivalent to an older and simpler concept., 4 pages

Objective To review the complex pathogenesis of the subdural membrane and the link between head trauma, dementia, and dural lymphatics. Methods A thorough literature search of published English-language articles was performed using PubMed, Ovid, and Cochrane databases. Results Chronic subdural hematoma (cSDH) is a common intracranial pathology and a leading cause of reversible dementia. cSDH is projected to affect at least 60,000 new individuals in the United States annually by 2030. This condition can result from mild to moderate head trauma that leads to hemorrhaging in the dura-arachnoid interface. The short-term and long-term effects of cSDH and the subdural membrane on the pathogenesis of dementia and the newly discovered dural lymphatics is a topic of increasing importance. Conclusions Further research into the possible link between traumatic brain injury and cSDH in particular and dural lymphatics and intracranial fluid dynamics is warranted.

BACKGROUND Traumatic brain injury (TBI) is a leading cause of death and disability in the United States. Educational interventions may alleviate the burden of TBI for patients and their families. Interactive modalities that involve engagement with the educational material may enhance patient knowledge acquisition when compared to static text-based educational material. OBJECTIVE To determine the effects of educational interventions in the outpatient setting on self-reported patient knowledge, with a focus on iPad-based (Apple, Cupertino, California) interactive modules. METHODS Patients and family members presenting to a NeuroTrauma clinic at a tertiary care academic medical center completed a presurvey assessing baseline knowledge of TBI or concussion, depending on the diagnosis. Subjects then received either an interactive iBook (Apple) on TBI or concussion, or an informative pamphlet with identical information in text format. Subjects then completed a postsurvey prior to seeing the neurosurgeon. RESULTS All subjects (n = 152) significantly improved on self-reported knowledge measures following administration of either an iBook (Apple) or pamphlet (P < .01, 95% confidence interval [CI]). Subjects receiving the iBook (n = 122) performed significantly better on the postsurvey (P < .01, 95% CI), despite equivalent presurvey scores, when compared to those receiving pamphlets (n = 30). Lastly, patients preferred the iBook to pamphlets (P < .01, 95% CI). CONCLUSION Educational interventions in the outpatient NeuroTrauma setting led to significant improvement in self-reported measures of patient and family knowledge. This improved understanding may increase compliance with the neurosurgeon's recommendations and may help reduce the potential anxiety and complications that arise following a TBI.

To evaluate the efficacy of otolaryngologist-performed in-office ultrasound (US) in the clinical assessment of lateral neck masses, we performed a retrospective review of patients with lateral neck masses who had both a surgeon-performed US and US-guided fine-needle aspiration (USGFNA) at our tertiary academic center from 2012 to 2015. Fifty-nine patients were included. USGFNA results included 32 (54%) malignant lesions, 23 (39%) benign lesions, and 4 (6%) nondiagnostic lesions. USGFNA demonstrated 85% accuracy. In 22 (37%) patients, in-office US revealed additional findings that were not identified on physical examination (eg, nonpalpable lymph nodes or elucidated anatomical structures), which either assisted in surgical planning or altered treatment. In-office US and USGFNA on initial evaluation by the otolaryngologist augment physical examination and have potential value as the primary imaging and diagnostic modality in the workup of lateral neck masses.

Author(s): Sahyouni, Ronald; Chang, David T; Moshtaghi, Omid; Mahmoodi, Amin; Djalilian, Hamid R; Lin, Harrison W | Abstract: Permanent injury to the cranial nerves can often result in a substantial reduction in quality of life. Novel and innovative interventions can help restore form and function in nerve paralysis, with bioelectric interfaces among the more promising of these approaches. The foreign body response is an important consideration for any bioelectric device as it influences the function and effectiveness of the implant. The purpose of this review is to describe tissue and functional effects of chronic neural implantation among the different categories of neural implants and highlight advances in peripheral and cranial nerve stimulation.Data Sources: PubMed, IEEE, and Web of Science literature search.Review Methods: A review of the current literature was conducted to examine functional and histologic effects of bioelectric interfaces for neural implants.Bioelectric devices can be characterized as intraneural, epineural, perineural, intranuclear, or cortical depending on their placement relative to nerves and neuronal cell bodies. Such devices include nerve-specific stimulators, neuroprosthetics, brainstem implants, and deep brain stimulators. Regardless of electrode location and interface type, acute and chronic histological, macroscopic and functional changes can occur as a result of both passive and active tissue responses to the bioelectric implant.A variety of chronically implantable electrodes have been developed to treat disorders of the peripheral and cranial nerves, to varying degrees of efficacy. Consideration and mitigation of detrimental effects at the neural interface with further optimization of functional nerve stimulation will facilitate the development of these technologies and translation to the clinic.3.

Objective To determine whether the use of in-office ultrasound (US) by a head and neck surgeon is a useful adjunct to clinical assessment of parotid lesions and decrease the need of additional imaging, such as magnetic resonance imaging (MRI) or computed tomography (CT). Study Design Case series with chart review. Setting Tertiary care academic center. Subjects Seventy patients presenting with a parotid lesion who obtained an in-office US and ultrasound-guided fine-needle aspiration (USGFNA) from a head and neck surgeon from 2006 to 2015. Methods US images were retrospectively reviewed for 70 patients and characterized by a radiologist and a head and neck surgeon. Results Of the 70 patients, 6 had US characteristics that demonstrated a statistically significant association with a benign/malignant diagnosis: depth from surface; irregular borders; presence of calcifications, which included either micro- or macro-calcifications; posterior echogenicity enhancement; irregular shape; and homogeneous/heterogeneous echotexture. Imaging was performed prior to referral in 25 cases (35.7%); of those, 17 (68%) were for superficial, small (

OBJECTIVESuccessful convection-enhanced delivery of therapeutic agents to subcortical brain structures requires accurate cannula placement. Stereotactic guiding devices have been developed to accurately target brain nuclei. However, technologies remain limited by a lack of MRI compatibility, or by devices’ size, making them suboptimal for direct gene delivery to brain parenchyma. The goal of this study was to validate the accuracy of a novel frameless skull-mounted ball-joint guide array (BJGA) in targeting the nonhuman primate (NHP) brain.METHODSFifteen MRI-guided cannula insertions were performed on 9 NHPs, each targeting the putamen. Optimal trajectories were planned on a standard MRI console using 3D multiplanar baseline images. After cannula insertion, the intended trajectory was compared to the final trajectory to assess deviation (euclidean error) of the cannula tip.RESULTSThe average cannula tip deviation was 1.18 ± 0.60 mm (mean ± SD) as measured by 2 independent reviewers. Topological analysis showed a superior, posterior, and rightward directional bias, and the intra- and interclass correlation coefficients were > 0.85, indicating valid and reliable intra- and interobserver evaluation.CONCLUSIONSThe data demonstrate that the BJGA can be used to reliably target subcortical brain structures by using MRI guidance, with accuracy comparable to current frameless stereotactic systems. The size and versatility of the BJGA, combined with a streamlined workflow, allows for its potential applicability to a variety of intracranial neurosurgical procedures, and for greater flexibility in executing MRI-guided experiments within the NHP brain.

This paper presents an improved design for waveguide based leaky wave antennas (LWAs) with discrete aperture to achieve a narrow beam and low sidelobe level (SLL). In this design a new formula for calculation of the required leakage constant is used. Then the geometrical parameters of the antenna are changed in such a way that the calculated leakage constant and a linear phase distribution are realized. Using the presented design method, a LWA with a Dolph_Chebyshev distribution, predefined sidelobe level of −30 dB and 9° beamwidth at 10 GHz is designed and simulated. Simulation results show a good agreement with theoretical results.

Chordoma, a rare bone tumor that occurs along the spine, has led scientists on a fascinating journey of discoveries. In this historical vignette, the authors track these discoveries in diagnosis and treatment, noting events and clinicians that played pivotal roles in our current understanding of chordoma. The study of chordoma begins in 1846 when Rudolf Virchow first observed its occurrence on a dorsum sellae; he coined the term “chordomata” 11 years later. The chordoma’s origin was greatly disputed by members of the scientific community. Eventually, Müller’s notochord hypothesis was accepted 36 years after its proposal. Chordomas were considered benign and slow growing until the early 1900s, when reported autopsy cases drew attention to their possible malignant nature. Between 1864 and 1919, the first-ever symptomatic descriptions of various forms of chordoma were reported, with the subsequent characterization of chordoma histology and the establishment of classification criteria shortly thereafter. The authors discuss the critical historical steps in diagnosis and treatment, as well as pioneering operations and treatment modalities, noting the physicians and cases responsible for advancing our understanding of chordoma.

BackgroundNeurological surgeons oftentimes educate patients and their families on complex medical conditions and treatment options. Time constraints and varied linguistic and cultural backgrounds limit the amount of information that can be disbursed. In this study, we assessed the linguistic validity of interactive educational interventions in non-English-speaking patients with traumatic brain injury (TBI) and concussion and their families.MethodsA total of 273 English-, Spanish-, Korean-, and Vietnamese-speaking neurotrauma patients (n=124) and family members (n=149) completed a presurvey to evaluate their incipient understanding, interacted with an iPad-based iBook (Apple) on concussion or TBI in their native language, completed a postsurvey to gauge changesin understanding, and then consulted with their neurosurgeon.ResultsAll participants (124 patients and 149 family members) had significantly increased (95% confidence interval [CI], P < 0.01) postsurvey scores (average pre-iBook score, 2.810; average post-iBook score, 4.109), regardless of native language or cultural background. Caucasian participants scored significantly higher than the combination of all ethnicities on both the baseline survey (95% CI, P < 0.01) and the post-iBook survey (95% CI, P&nbsp

OBJECTIVE: To discuss the state-of-the-art with regards to established or promising bioelectric therapies meant to alter or control neurologic function. We present recent reports on bioelectric technologies that interface with the nervous system at three potential sites – (1) the end organ, (2) the peripheral nervous system, and (3) the central nervous system – while exploring practical and clinical considerations. DATA SOURCES: Pubmed, IEEE, and Web of Science literature search. REVIEW METHODS: A review of the current literature was conducted to examine functional and histomorphological effects of neuroprosthetic interfaces with a focus on end-organ, peripheral, and central nervous system interfaces. CONCLUSIONS: Innovations in bioelectric technologies are providing increasing selectivity in stimulating distinct nerve fiber populations in order to activate discrete muscles. Significant advances in electrode array design focus on increasing selectivity, stability, and functionality of implantable neuroprosthetics. IMPLICATIONS FOR PRACTICE: The application of neuroprosthetics to paretic nerves or even directly stimulating or recording from the central nervous system holds great potential in advancing the field of nerve and tissue bioelectric engineering and contributing to clinical care. Although current physiotherapeutic and surgical treatments seek to restore function, structure, or comfort, they bear significant limitations in enabling cosmetic or functional recovery. Instead, the introduction of bioelectric technology may play a role in the restoration of function in patients with neurologic deficits.

Background This review aims to highlight the clinical complexity of chronic subdural hematoma (cSDH) while presenting a brief historical discussion of cSDH. Methods A thorough literature search of published English-language papers was performed in PubMed, Ovid, and Cochrane databases. Results cSDH affects 1–5.3 per 100,000 individuals annually, with the incidence expected to rise as the U.S. population ages. The symptoms of cSDH are often nonspecific, with headaches being the most common complaint. Other symptoms include weakness, balance and gait problems, and memory problems. Conclusions A variety of clinical factors must be taken into account in the treatment of cSDH, and the multifaceted treatment paradigms continue to evolve.

We shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise $w^*$-approximate Connes amenability, for dual Banach algebras which take the $w^*$-topology into account. We shall study these concepts for the Banach sequence algebras $\ell^1(\omega)$ and the weighted semigroup algebras $ \ell^{1}(\mathbb{N}_{\wedge},\omega)$. For a weight $\omega$ on a discrete semigroup $S$, we shall investigate pointwise amenability/Connes amenability of $\ell^1(S,\omega)$ in terms of diagonals., Comment: 9 pages

ObjectivesTraumatic Brain Injury (TBI) is a common and debilitating injury that is particularly prevalent in patients over 60. Given the influence of head injury on dementia (and vice versa), and the increased likelihood of ground-level falls, elderly patients are vulnerable to TBI. Educational interventions can increase knowledge and influence preventative activity to decrease the likelihood of further TBI. We sought to determine the efficacy of interactive tablet-based educational interventions in elderly patients on self-reported knowledge.Patients and methodsPatients and family members, ages 20-90, presenting to a NeuroTrauma clinic completed a pre-survey to assess baseline TBI or concussion knowledge, depending on their diagnosis. Participants then received an interactive electronic book (eBook), or a text-based pamphlet with identical information, and completed a post-survey to test interim knowledge improvement.ResultsAll participants (n=180), regardless of age, had significantly higher post-survey scores (p

IntroductionPhysicians in the ambulatory setting face challenges in adequately educating patients in a brief office encounter.ObjectiveTo evaluate the efficacy of an iPad-based interactive educational module (iBook) in various otologic pathologies.MethodsPatients presenting with symptoms of tinnitus, dizziness, hearing loss, or cochlear implant evaluation were included. In total, 44 patients received the iBook and 22 patients served as controls. Prior to viewing the iBook, patients completed a pre-survey to assess baseline knowledge. After viewing the iBook, patients completed a post-survey to assess changes in perception and knowledge of their disease. Results were compared to that of the control group who did not receive iBook supplementation prior to being seen by the physician.ResultsPaired t-test analysis showed significant improvements (p

In this article, we study the following fractional boundary value problem D 0 + α c u ( t ) + 2 r D 0 + α − 1 c u ( t ) + r 2 D 0 + α − 2 c u ( t ) = f ( t , u ( t ) ) , r > 0 , 0

Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let @l be an eigenvalue of A with multiplicity m"A(@l). An edge e=ij is said to be Parter (resp., neutral, downer) for @l,A if m"A(@l)-m"A"-"e(@l) is negative (resp., 0, positive ), where A-e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue @l of A, if |S|=m"A(@l) and A-S has no eigenvalue @l. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is proved. We prove that neutral edges always exist for eigenvalues of multiplicity more than 1. It is also proved that an edge e=uv is a downer edge for @l,A if and only if u and v are both downer vertices for @l,A; and e=uv is a neutral edge if u and v are neutral vertices. Among other results, it is shown that any edge star set for each eigenvalue of a tree is a matching.

Let $G$ be a locally compact group and $omega$ be a symmetric weight function on $G$. We define a co-product $Gamma_omega$ on the weighted algebra $L^infty(G, omega^{-1})$ of essentially $omega$-bounded Borel measurable functions on $G$ and show that $L^infty(G, omega^{-1})$ becomes a Kac algebra with natural co-inverse $kappa_omega$ and Haar weight $phi_omega$. We use the machinery of Kac algebras to introduce the weighted Fourier and Fourier-Stieltjes algebra $ A(G,omega^{-1})$ and $ B(G,omega^{-1})$ of $G$.

In this paper we study graphs all of whose star sets induce cliques or co-cliques. We show that the star sets of every tree for each eigenvalue are independent sets. Among other results it is shown that each star set of a connected graph G with three distinct eigenvalues induces a clique if and only if G = K 1 , 2 or K 2 , … , 2 . It is also proved that stars are the only graphs with three distinct eigenvalues having a star partition with independent star sets.

We prove that L p (G) is super-amenable if and only if G is finite. We denote the space of all weakly almost periodic functions on a locally com- pact group G ,b y WA P(G). We show that the dual Banach algebra WA P(G) ∗ is Connes-amenable if and only if G is amenable. However, it is proved in ( Run 5), but our proof is different. If G is amenable and ω is a diagonally bounded weight function on G, then M(G, Ω) has a normal, virtual diagonal. Mathematics Subject Classification: Primary: 22D15, 43A10; Sec- ondary: 43A20, 46H25, 47B47 1. Super-amenability of L p (G) In the throughout this section, G is a compact group, so that λ(G) < ∞. Let p ∈ (1, ∞). In the case L p (G) is a Banach algebra with the convolution product.

Suppose A is a presumably if intransitive commutative Banach algebra in its second dual A **. The paper studied several weaker definitions on amenability, Connes amenability including quotient pointwise amenability and approximate Connes amenability. Furthermore, the relations between them were discussed.