Firstly by adding the new condition with unknown parameter in

Firstly by adding the new condition with unknown parameter α in the boundary conditions (2.6) and splitting intowhere u(a)=b is called the forcing condition that PD 0332991 comes from original conditions (2.6). By calculating variation with respect to u(τ) for variational iteration formula (2.2) on the problem (2.5) with the new initial conditions (2.7), the Lagrange multiplier λ(τ) can be identified as (He, 1998; He, 1999; Wazwaz, 2007; Wazwaz, 2009)then the iteration formula (2.4) becomes
It should be emphasized that u(t,α,h) can be computed by symbolic software programs such as Mathematica or Maple, starting by an initial approximation u0(t,α) which satisfies at least the initial conditions (2.7). We obtain the approximate solution u(t,α,h) for the problem (2.5) and (2.7), but there are still two unknown parameters in the approximate solution u (t,α,h) the unknown parameter α and the auxiliary parameter h, should be determined. The forcing condition (2.8) of the boundary value problem (2.5) reads
The Eq. (2.11) has two unknown parameters α and h which control the approximation u(t,α,h) that converges to the exact solution. According to Eq. (2.11), α as function of h, by drawing the Eq. (2.11) gives the so called h-curve. The number of such horizontal plateaus where α(h) becomes constant, gives the multiplicity of the solutions. Also the horizontal plateaus indicate the convergence because the unknown parameter α is a constant value then a horizontal line segment in h-curve which corresponds to the valid region of h.

Applications

Conclusions

Introduction
In the sequence of these integral transforms, the Laplace – type integral transform, so-called transform, is defined for a squared and an exponential function by David et al. (2007), asThe transform is related to the classical Laplace transform by means of the following relationships :andLet f and g be Lebesgue integrable functions; then the operation between f and g is defined byThe operation is commutative, associative and satisfies the equation .
Some facts about the transform are given as follows:
More properties, applications and the inversion formula of transform are given by Yürekli (1999a,b).

Abstract construction of Boehmians
The minimal structure necessary for the construction of Boehmians consists of the following elements :
ConsiderIf , then we say . The relation is an equivalence relation in . The space of equivalence classes in is denoted by . Elements of are called Boehmians.
Between and there is a canonical embedding expressed asThe operation can be extended to byThe sum of two Boehmians and multiplication by a scalar can be defined in a natural wayandThe operation and the differentiation are defined byandIn particular, if and is any fixed element, then the product , defined byis in .
Many a time is also equipped with a notion of convergence. The intrinsic relationship between the notion of convergence and the product is given by:
In , two types of convergence are:
The following theorem is equivalent to the statement of – convergence :
For further discussion of Boehmian spaces and their construction; see Ganesan (2010), Karunakaran and Ganesan (2009), Al-Omari (2012, 2013a,b,c,d), Al-Omari and Kilicman (2011, 2012a,b, 2013a,b), Boehme (1973), Bhuvaneswari and Karunakaran (2010), Ganesan (2010), Karunakaran and Angeline (2011), Karunakaran and Devi (2010), Mikusinski (1983, 1987, 1995), Nemzer (2006, 2007, 2008, 2009, 2010) and Roopkumar (2009).

denotes the space of rapidly decreasing functions defined on . That is, if is a complex-valued and infinitely smooth function defined on and is such that, as and its partial derivatives decrease to zero faster than every power of .
In more details, iff it is infinitely smooth and is such thatm and k run through all non-negative integers; see Pathak (1997).
denotes the Schwartz space of test functions of bounded support defined on .
denotes the Mellin-type convolution product offirst kind defined by Zemanian (1987), asTo construct the first Boehmian space , we need to establish the following necessary theorems.

br Discussion In comparison to thoracotomy or

Discussion
In comparison to thoracotomy or blind injection, the usual methods for intrathymic injections in mice, free-hand ultrasound-guided injection appears to be a safe, fast and highly accurate alternative. In our past experience, ultrasound-guided mouse intrathymic injections using the rail platform required about 10 minutes per injection, whereas the interventional radiologist was able to accomplish the injection in about 10 seconds for young mice and about 20 seconds for older or immunodeficient mice. Another advantage of this free-hand approach is that it also avoids the limitations associated with rigidity of the ultrasound imaging station, enabling the radiologist to not only to reduce the injection period significantly, but also to inject either the left or right lobe (or both) accurately. Injection of individual lobes has the potential to reduce the number of individual experimental subjects, because in each mouse one lobe could be subjected to placebo injection while the other lobe received an experimental injection. Importantly, cross-talk between thymic lobes does not occur (Matsuzaki et al. 1993). To perform injections in both thymic lobes using the imaging station, the needle injection attachment would have to be dismounted, transferred to the opposite side and remounted, resulting in considerably increased anesthesia time for each injection.
The ability to accurately inject the small, involuted thymi of older mice introduces the potential for a wide range of studies concerning the utility of intrathymic injection in assisting with immune reconstitution in adult diseases. It should, however, be noted that in humans, in PD 0332991 to mice, thymic involution is associated with replacement of thymic tissue by interdigitating adipose tissue (Chinn et al. 2012), making identification of bioactive thymic tissue more challenging.
Our method for intrathymic injection may even have potential for clinical translation; among others, progenitor T cell injection may be a promising candidate for intrathymic injection-based therapies. Mouse progenitor T cells leave the bone marrow and home to the thymus where they develop into mature, naïve T cells. These progenitor cells travel to the thymus during a responsive period based on specific chemokine signaling (Donskoy et al. 2003; Foss et al. 2001). During a refractory period lasting 3 of every 4 weeks, progenitor T cells cannot home to the thymus, and thymic T cell production is significantly reduced (Foss et al. 2001). It is hypothesized that direct injection of progenitor T cells into the thymus may facilitate continuous T cell production, even during refractory periods and without reliance on chemokines. Of note, our findings in NSG mice suggest that the thymi of these mice can be targeted by ultrasound-guided injections, indicating that our technique could considerably facilitate intrathymic injection-based studies in mouse models of SCID. Several previous studies have reported that delivery of healthy bone marrow cells to the thymi of mice with defective T cell development can establish long-lasting T cell generation, underscoring the clinical relevance of this approach (Adjali et al. 2005b; Vicente et al. 2010). Finally, no major complications were observed during this study; there were no procedure-related deaths and only two symptomatic complications in the course of more than 400 subsequent thymus injections that were performed for this and other studies (Tuckett et al. 2014); both were instances of hindleg paralysis, presumably related to air embolism from the injection procedure. In one other case, a mediastinal hematoma was observed immediately after injection, but there was no clinical correlate to this imaging finding.

Conclusions

Acknowledgments
This research was supported by National Institutes of Health Awards R01 HL069929 (M.R.M.v.d.B.) and K08 CA160659 (J.L.Z.). Technical services provided by the Memorial Sloan Kettering Cancer Center Small-Animal Imaging Core Facility, supported in part by NIH Cancer Center Support Grant 2 P30 CA008748-48, are gratefully acknowledged.

The paired sensory features belong to one stimulus in the

The paired sensory features belong to one stimulus in the studies on contingent aftereffects. The color of the grating is contingent upon the orientation of the same grating. However, the perception of a visual object is largely influenced not only by the stimulus features belonging to the object itself but also by its surroundings. For instance, the perceived brightness and color of an object depend upon its surroundings (Albright & Stoner, 2002). The perceived shape (Kaufman, 1979) and moving velocity and direction (Loomis & Nakayama, 1973; Nawrot & Sekuler, 1990) of an object are also influenced by its surroundings. It is possible that the aftereffects are also affected by spatial contexts. It was recently shown that the tilt aftereffects could be contingent on the features of the surrounding frames, and that these effects lasted for 24h (Nakashima & Sugita, 2014). It has been reported that the motion aftereffects (MAE) are contingent on the color of the surroundings (Durgin, 1996; Potts & Harris, 1975). Therefore, in this study, we examined whether the MAE were affected by spatial contexts and found that the MAE could be contingent on the shape of the surrounding frames and the effects persisted at least for 24h.
Motion and form information is strongly linked in the brain: some neurons in the visual PD 0332991 are selective for both motion and orientation (Albright, 1984; Maunsell & Van Essen, 1983) and distinct pathways of motion and form mutually interact (Beck & Neumann, 2010). Recent psychophysical studies have demonstrated that motion and form perception interact. The strength of the MAE is modulated by orientation signals presented with motion stimuli, and the motion–orientation interaction is considered to occur at the higher level of motion processing where local motion is integrated (Mather, Pavan, Bellacosa, & Casco, 2012) or optic flow is extracted (Pavan, Marotti, & Mather, 2013). The frame shape-contingent MAE examined in the present study demonstrates another type of motion-form interaction where motion and shape signals interact.
It has been argued that some aftereffects are remapped across a saccade to keep the adapting location aligned in the external world (Melcher, 2005, 2007; Zimmermann, Morrone, Fink, & Burr, 2013), although the aftereffects are the strongest in the retinotopic reference frame. The MAE were found to occur in the spatiotopic reference frame (Ezzati, Golzar, & Afraz, 2008). However, it has been also reported that the MAE are retinotopic but not spatiotopic (Knapen, Rolfs, & Cavanagh, 2009; Wenderoth & Wiese, 2008). The results of fMRI studies have been also inconsistent. One study claimed that the area hMT encodes motion signals not only in the retinotopic but also in the spatiotopic position (d’Avossa et al., 2007); however, it has also been reported that only retinotopic representation is observed in the MT (Gardner, Merriam, Movshon, & Heeger, 2008). To examine the reference frame of the contingent MAE, we conducted experiments with four reference frame conditions where the location of adapter and test stimuli were: the same in a retinotopic frame of reference (retinotopic), the same in a spatiotopic frame of reference (spatiotopic), the same in both frames of reference (full), and different in both frames of reference (unmatched).

Experiment 1

Experiment 2
In Section 2, the inner side of the square frame (4.3°) was smaller than the diameter of the circular window (4.6°) where the motion stimulus was presented to make the motion window itself square. The square frame overlapped with the outer part of the motion window, whereas the circle frame did not. The differential aftereffects might be due to the changing boundary of the motion stimulus. In Section 3, we conducted a similar experiment, reducing the size of the motion window to avoid overlap.

Discussion
The contingent MAE have been demonstrated for such a stimulus that contains both paired stimulus features. For example, in the color-contingent MAE, the motion of a spiral stimulus is contingent on the color of the same spiral (Favreau et al., 1972). The present study demonstrated that the MAE could be contingent upon an induction stimulus presented outside the test stimulus. It has been widely considered that the contingent aftereffects require joint encoding of the parameters to be linked (Barlow, 1990; Braddick, Campbell, & Atkinson, 1978). It is known that the visual perception of an object is influenced not only by the stimulus features that belong to the object itself but also by its surroundings (Albright & Stoner, 2002; Kaufman, 1979). A number of studies have shown PD 0332991 that the stimuli presented outside the receptive fields strongly modulate the activity of cortical visual cells (Blakemore & Tobin, 1972; Gilbert & Wiesel, 1990; Knierim & van Essen, 1992; Lamme, 1995; Sillito, Grieve, Jones, Cudeiro, & Davis, 1995). These cells might be responsible for the surround-contingent aftereffects.

Phase I corresponds to the time when

Phase I corresponds to the time when the heart, or cardiac muscle, pulsates. Fig. 12 depicts (a) the averaged acceleration map of the 24-year-old male subject at a fixed depth, (b) a close-up of the acceleration map, and (c) phase versus width of the pulse wave and the regression line. The mean PWV of phase I for three measurements was 3.52±1.11m/s. The correlation coefficient was 0.9604±0.015.
Phase II corresponds to the time when the tricuspid and mitral valves close, and the aortic and pulmonic valves open. Fig. 13 depicts (a) the averaged acceleration map of the 24-year-old male subject at a fixed depth, (b) a close-up of the acceleration map, and (c) phase versus width of the pulse wave and the regression line. The mean PWV of Phase II for three measurements was to 5.62±0.30m/s. The correlation coefficient was 0.9570±0.015.
Fig. 14 depicts (a) the averaged acceleration map of the 24-year-old male subject at a fixed depth, (b) a close-up of the acceleration map, and (c) phase versus width of the pulse wave and the regression line. The wave of Fig. 14 (b) traveled in the reverse direction from the distal artery to the proximal artery, indicating that this was a reflective wave. The mean PWV of the reflective wave for three measurements was −4.60±0.99m/s. The correlation coefficient was 0.846±0.069. However, the PWV of the reflective wave was lower than previously reported [7]. It is necessary to determine the difference between the measured PWV and the reported PWV.
Phase III (dicrotic notch) corresponds to the time when the tricuspid and mitral valves open, and the aortic and pulmonic valves close. A dicrotic notch reflects systemic vascular resistance. The dicrotic notch disappears for peripheral vascular resistance PD 0332991 like blood poisoning. Fig. 15 depicts (a) the averaged acceleration map of the 24-year-old male subject at a fixed depth, (b) a close-up of the acceleration map, and (c) phase versus width of the pulse wave and the regression line. The mean PWV of phase III for three measurements was 7.94±0.85m/s. The correlation coefficient was 0.979±0.005.
Fig. 16 summarizes the quantitative PWV measurements. Triangles denote the estimated PWV value for phase I, diamonds denote that for phase II, squares denote that for phase III, and dots denote that for the reflective wave. The error bar indicates the standard deviation of the PWV of each subject for each phase. The dashed line denotes the mean value of the whole PWV for each phase. PWVs in phase I and the reflective wave were occasionally not observed. The mean PWV in phase II was 5.38–6.03m/s, and the mean value of all subjects was 5.62m/s (r=0.937±0.025). The mean PWV in phase III was 6.99–9.20m/s, which was higher than that in phase II, and the mean value of all subjects was 7.94m/s (r=0.948±0.008).
Fig. 17 presents the results of the two-dimensional displacement vector at four points in the anterior wall of the artery during one heartbeat. Fig. 17(a) depicts lateral displacement and axial displacement, and Fig. 17(b) depicts the relationship between lateral and axial displacements. A dot corresponds to the start time of deformation induced by pulsation. The direction of the deformation is anticlockwise (black arrows). These results conformed to past research [30,31]. Fig. 18 summarizes the analysis of lateral wall motion of the 24-year-old male subject early in the phase. The color map corresponds to the amplitude of the two-dimensional vector, and the arrows correspond to the amplitude of the lateral component of the vector. Fig. 18 presents (a) a spatial compound image of the artery overlaid with the velocity and (b)–(f) close-up images of the velocity at the region of interest. The time of Fig. 18(f) corresponds to the arrival time of blood ejected from the left ventricle (Fig. 8(a)). The timing of each image is (b) 4ms earlier, (c) 3ms earlier, (d) 2ms earlier, and (e) 1ms earlier.

br Our study demonstrated that the

Our study demonstrated that the average excursions of the bilateral PD 0332991 during tidal breathing (right: 11.0 mm, 95% CI 10.4 to 11.6 mm; left: 14.9 mm, 95% CI 14.2 to 15.5 mm) were numerically less than those during forced breathing in previous studies using other modalities 2; 7 ;  8. Using fluoroscopy, Alexander reported that the average right excursion was 27.5 mm and the average left excursion was 31.5 mm during forced breathing in the standing position in 127 patients (2). Using ultrasound, Harris et al. reported that the average right diaphragm excursion was 48 mm during forced breathing in the supine position in 53 healthy adults (7). Using MR fluoroscopy, Gierada et al. reported that the average right excursion was 44 mm and the average left excursion was 42 mm during forced breathing in the supine position in 10 healthy volunteers (8). The difference in diaphragmatic excursion during tidal breathing versus forced breathing is unsurprising.

Our study showed that the excursion and peak motion speed of the left diaphragm are significantly greater and faster than those of the right. With regard to the excursion, the results of our study are consistent with those of previous reports using fluoroscopy in a standing position 2 ;  3. However, in the previous studies evaluating diaphragmatic motion in the supine position, the asymmetric diaphragmatic motion was not mentioned 7 ;  8. The asymmetric excursion of the bilateral diaphragm may be more apparent in the standing position, but may not be detectable or may disappear in the supine position. Although we cannot explain the reason for the asymmetry in diaphragmatic motion, we speculate that the presence of the liver may limit the excursion of the right diaphragm. Regarding the motion speed, to the best of our knowledge this study is the first to evaluate it. The faster motion speed of the left diaphragm compared to that of the right diaphragm would be related to the greater excursion of the left diaphragm.

We found that higher BMI and higher tidal volume were independently associated with the increased excursions of the bilateral diaphragm by both univariate and multivariate analyses, although the strength of these associations was weak. We cannot explain the exact reason for the correlation between BMI and the excursion of the diaphragm. However, a previous study showed that BMI is associated with peak oxygen consumption (23), and the increased oxygen consumption in an obese participant may affect diaphragmatic movement. Another possible reason is that lower thoracic compliance due to higher BMI may cause increased movement of the diaphragm for compensation. Regarding the correlation between tidal volume and excursion of the diaphragm, given that diaphragmatic muscle serves as the most important respiratory muscle, the result is to be expected. Considering our results, the excursion evaluated by dynamic X-ray phrenicography could potentially predict tidal volume.

Our study has several limitations. First, we included only 172 volunteers, and additional studies on larger participant populations are required to confirm these preliminary findings. Second, we evaluated only the motion of the highest point of the diaphragms for the sake of simplicity, and three-dimensional motion of the diaphragm could not be completely PD 0332991 reflected in our results. However, we believe that this simple method would be practical and more easily applicable in a clinical setting.

Conclusions

The time-resolved quantitative analysis of the diaphragms with dynamic X-ray phrenicography is feasible. The average excursions of the diaphragms are 11.0 mm (right) and 14.9 mm (left) during tidal breathing in a standing position in our health screening center cohort. The diaphragmatic motion of the left is significantly larger and faster than that of the right. Higher tidal volume and BMI are associated with increased excursions of the bilateral diaphragm.

The concentrations of V Cd and Ba were under

The concentrations of V, Cd and Ba were under the detection limit, but it PD 0332991 is not known if there is some presence of these elements in the VRS at very low levels. Hg concentrations in H. aurolineatum were highest in the North reef group with median concentration of 2.29, and 1.83 μg/g in the South group. It is interesting that H. aurolineatum presents higher Hg concentrations compared with O. chrysurus in the same zones. One possible explanation is that H. aurolineatum presents a different behavior than O. chrysurus; H. aurolineatum takes nocturnal migrations away from their daytime habitats to forage, feeding close to grass and sand flats, and their feeding behavior is less associated with coral habitats than the other grounds. The higher Hg accumulation could be related with these movements and the possibility that Hg concentrations are higher in their feeding areas that in the reef itself. The Natural Resource Defense Council (NRDC) has classified snappers, like O. chrysurus, as moderate Hg accumulators, and other authors have reported that grunt species, such as H. aurolineatum, are higher Hg accumulators, at the level of top predators such as sharks and barracudas ( Mol et al., 2001; Ploetz et al., 2007; De Castro Rodrigues et al., 2010; De Castro Rodrigues et al., 2011; Costa and Lacerda, 2014 ; Zuluaga Rodríguez et al., 2015).
Selenium has a protective effect on mercury toxicity, and the two are often correlated. At high concentrations, selenium has a protective effect on mercury toxicity (Burger et al., 2001). In this study a negative correlation was observed, being more notorious in Ocyurus chrysurus than in H. aurolineatum.
It is interesting that when comparing hydrocarbon concentrations between the two reef groups all the significantly higher values were in the North reef group, and this was even more evident with PD 0332991 O. chrysurus. The North group is characterized by the presence of untreated sewage discharges and it is also a zone of discharge of ship waste, thus the presence of hydrocarbon is expected. Concentrations of high molecular weight PAH, aliphatics, UCM and total hydrocarbons were significantly higher for O. chrysurus in this zone. The presence of these pollutants can be related with the high ship traffic in this particular zone, which also has urban discharges, and atmospheric inputs from the main city of Veracruz and other urbanized areas around the study area ( Soclo et al., 2000). For pollutant concentrations in liver of O. chrysurus, these higher concentrations could also be related with age.
PAH exposure induces phase I and II enzymatic detoxification to produce more polar and easily excreted metabolites, and transcript abundance of CYP1A and GsT, both involved in xenobiotic metabolism, were well represented with a high correlation with hydrocarbon concentrations. Both species showed different levels of expression ( Fig. 2). For H. aurolineatum the results do not present significant statistical differences when comparing the transcript abundances of CYP, GsT and VTG; this result suggests acclimatization of this species to local stress conditions, different exposures or exposure routes ( Fonseca et al., 2011). O. chrysurus presents highly significant transcript abundance for GsT, CYP1A and VTG in the North reef group; CYP1A and GsT are known to be induced by various organic pollutants in fish ( Nahrgang et al., 2010 ; Sarkar et al., 2006).
VTG gene expression in O. chrysurus males was higher than that for O. chrysurus females in the North group, suggesting that these fish were exposed to endocrine disrupting compounds that have affected their reproductive system. This could be related with oestrogenic compounds from urban discharges from Veracruz City and other urban areas in its vicinity, or other endocrine-disrupting pollutants not analyzed in this study. The analysis of endocrine-disrupting pollutants would be desirable in future studies to confirm this.