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Malnutrition significantly hampers wound healing processes. This study aimed to compare the effectiveness of the Global Leadership Initiative on Malnutrition (GLIM) and Subjective Global Assessment (SGA) in diagnosing malnutrition and predicting wound healing in patients with diabetic foot ulcers (DFU). GLIM criteria were evaluated for sensitivity (SE), specificity (SP), positive predictive value, negative predictive value and kappa (κ) against SGA as the reference. Modified Poisson regression model and the DeLong test investigated the association between malnutrition and non-healing ulcers over 6 months. This retrospective cohort study included 398 patients with DFU, with a mean age of 66·3 ± 11·9 years. According to SGA and GLIM criteria, malnutrition rates were 50·8 % and 42·7 %, respectively. GLIM criteria showed a SE of 67·3 % (95 % CI 60·4 %, 73·7 %) and SP of 82·7 % (95 % CI 76·6 %, 87·7 %) in identifying malnutrition, with a positive predictive value of 80·0 % and a negative predictive value of 71·1 % (κ = 0·50) compared with SGA. Multivariate analysis demonstrated that malnutrition, as assessed by SGA, was an independent risk factor for non-healing (relative risk (RR) 1·84, 95 % CI 1·45, 2·34), whereas GLIM criteria were associated with poorer ulcer healing in patients with estimated glomerular filtration rate ≥ 60 ml/min/1·73m2 (RR: 1·46, 95 % CI 1·10, 1·94). SGA demonstrated a superior area under the receiver’s operating characteristic curve for predicting non-healing compared with GLIM criteria (0·70 (0·65–0·75) v. 0·63 (0·58–0·65), P < 0·01). These findings suggest that both nutritional assessment tools effectively identify patients with DFU at increased risk, with SGA showing superior performance in predicting non-healing ulcers.
We report an experimental study of the formation and evolution of laminar thermal structures generated by a small heat source, with a focus on their correlation to the thermal boundary layer and effects of heating time $t_{heat}$. The experiments are performed over the flux Rayleigh number ($Ra_f$) range $2.1\times 10^6 \leq Ra_f \leq 3.6\times 10^{7}$ and the Prandtl number ($Pr$) range $28.6 \leq Pr \leq 904.7$. The corresponding Rayleigh number ($Ra= t_{heat}\,Ra_{f}/\tau _0\,Pr$) range is $900 \leq Ra \leq 4\times 10^{4}$, where $\tau _0$ is a diffusion time scale. For thermal structures generated by continuous heating (i.e. starting plumes), their formation process exists three characteristic times that are well reflected by changes in the thermal boundary layer thickness. These characteristic times, denoted as $t_{emit}$, $t_{recover}$ and $t_{static}$, correspond to the moments when the plume emission begins and completes, and when the thermal boundary layer becomes quasi-static, respectively. Their $Ra_f$–$Pr$ dependencies are found to be $t_{emit}/\tau _0\sim Ra_f^{-0.41}\,Pr^{0.41}$, $t_{recover}/\tau _0\sim Ra_f^{-0.48}\,Pr^{0.48}$ and $t_{static}/\tau _0\sim Ra_f^{-0.49}\,Pr^{0.33}$, respectively. Thermal structures generated by finite $t_{heat}$ exhibit similar evolution dynamics once $t_{heat} \ge t_{emit}$, with the accelerating stage behaving like starting plumes and the decay stage like thermals (i.e. a finite amount of buoyant fluids). It is further found that their maximum rising velocity experiences a transition in the $Ra$-dependence from $Ra$ to $(Ra\ln Ra)^{0.5}$ at $Ra \simeq 6000$; and their maximum acceleration reaches the value of starting plumes at $t_{heat}\simeq t_{recover}$, and remains unchanged for larger $t_{heat}$. In particular, the maximum rising velocity for the cases with $t_{heat} = t_{recover}$ follows a scaling relation $Ra_f^{0.37}\,Pr^{-0.37}$, in contrast to the relation $Ra_f^{0.48}\,Pr^{-0.48}$ for starting plumes. This study provides a more comprehensive understanding of laminar thermal structures, which are relevant to a range of processes in nature and laboratory systems such as Rayleigh–Bénard convection.
Sulfonated carbon is a ‘green,’ solid-acid catalyst. For applications purposes, its surface area needs to be improved and its preparation needs to be made environmentally friendly. The objective of the present study was to provide a green and economical method of preparing a sulfonated carbon catalyst by using palygorskite (Plg) fiber as a support for sulfonated carbon. Sulfonated carbon/palygorskite solid-acid catalyst (SC-Plg) was synthesized via one-step carbonization-sulfonation by mixing palygorskite with sucrose as the carbon source and p-toluenesulfonic acid as the sulfonating agent. The catalyst was characterized by SEM, EDX, TEM, FTIR, and nitrogen adsorption-desorption isotherms. The results indicated that sucrose-derived carbon was loaded uniformly on the surface of Plg fibers and formed the SC-Plg catalyst. The inexpensive Plg fibers could replace sucrose-derived carbon and increase the surface area of the resulting catalyst. The SC-Plg shows significant catalytic performance and excellent stability when used in the esterification of oleic acid with methanol. The conversion of oleic acid reached 68.09%, even after five cycles. This work paves the way for the development of highly active, carbon-based, solid-acid composite catalysts using a natural Plg nanofiber template.
The objective of this study was to understand and measure epigenetic changes associated with the occurrence of CHDs by utilizing the discordant monozygotic twin model. A unique set of monozygotic twins discordant for double-outlet right ventricles (DORVs) was used for this multiomics study. The cardiac and muscle tissue samples from the twins were subjected to whole genome sequencing, whole genome bisulfite sequencing, RNA-sequencing and liquid chromatography-tandem mass spectrometry analysis. Sporadic DORV cases and control fetuses were used for validation. Global hypomethylation status was observed in heart tissue samples from the affected twins. Among 36,228 differentially methylated regions (DMRs), 1097 DMRs involving 1039 genes were located in promoter regions. A total of 419 genes, and lncRNA–mRNA pairs involved 30 genes, and 62 proteins were significantly differentially expressed. Multiple omics integrative analysis revealed that five genes, including BGN, COL1A1, COL3A1, FBLN5, and FLAN, and three pathways, including ECM-receptor interaction, focal adhesion and TGF-β signaling pathway, exhibited differences at all three levels. This study demonstrates a multiomics profile of discordant twins and explores the possible mechanism of DORV development. Global hypomethylation might be associated with the risk of CHDs. Specific genes and specific pathways, particularly those involving ECM–receptor interaction, focal adhesion and TGF–β signaling, might be involved in the occurrence of CHDs.
Behavioral addiction (BA) and substance use disorder (SUD) share similarities and differences in clinical symptoms, cognitive functions, and behavioral attributes. However, little is known about whether and how functional networks in the human brain manifest commonalities and differences between BA and SUD. Voxel-wise meta-analyses of resting-state functional connectivity (rs-FC) were conducted in BA and SUD separately, followed by quantitative conjunction analyses to identify the common and distinct alterations across both the BA and SUD groups. A total of 92 datasets with 2444 addicted patients and 2712 healthy controls (HCs) were eligible for the meta-analysis. Our findings demonstrated that BA and SUD exhibited common alterations in rs-FC between frontoparietal network (FPN) and other high-level neurocognitive networks (i.e. default mode network (DMN), affective network (AN), and salience network (SN)) as well as hyperconnectivity between SN seeds and the Rolandic operculum in SSN. In addition, compared with BA, SUD exhibited several distinct within- and between-network rs-FC alterations mainly involved in the DMN and FPN. Further, altered within- and between-network rs-FC showed significant association with clinical characteristics such as the severity of addiction in BA and duration of substance usage in SUD. The common rs-FC alterations in BA and SUD exhibited the relationship with consistent aberrant behaviors in both addiction groups, such as impaired inhibition control and salience attribution. By contrast, the distinct rs-FC alterations might suggest specific substance effects on the brain neural transmitter systems in SUD.
High-molecular-weight glutenin subunits (HMW-GS) contribute to dough elasticity and bread baking quality in wheat. In this study, wheat varieties were classified based on their HMW-GS composition into three groups: 1Dx5 (5 + 10, Gaoyou 8901, Xinmai 28, Xinmai 19, Xinmai 26 and Jinbaoyin), 1Dx2 (2 + 12, Zhoumai 24, Xinmai 9 and Yumai) and 1Dx4 (4 + 12, Aikang 58). Sequence analysis showed that 1Dx-GY8901, 1Dx-XM28, 1Dx-XM19 and 1Dx-XM26 were similar to the 1Dx5 gene and clustered on the same branch, while 1Dx-AK58, 1Dx-ZM24, 1Dx-JBY, 1Dx-YM, 1Dx-XM9 and 1Dx-JBY were more similar to the 1Dx2 gene and clustered on the same branch with 1Dx.2.2. There was a mutation of Ser to Cys at position S2, for an extra Cys in the repeat regions of 1Dx-XM19, 1Dx-XM26, 1Dx-XM28 and 1Dx-GY8901. The wheat HMW-GS genes exhibited similar percentages of α-helix, extended strand, β-turn and random coil structure, with ranges of 13.33–13.59, 4.77–5.78, 7.08–9.18 and 72.3–73.94%, respectively. Sequence conservation and the composition of HMW-GS subunits were also analysed for a series of strong gluten wheat varieties, Xinmai 9 (1, 7 + 8, 2 + 12), Xinmai 19 (1, 7 + 9, 5 + 10), Xinmai 26 (1, 7 + 8, 5 + 10) and Xinmai 28 (1, 7 + 9, 5 + 10). The results of this work should facilitate future breeding efforts and provide the theoretical basis for wheat quality improvement.
Previous analyses of grey and white matter volumes have reported that schizophrenia is associated with structural changes. Deep learning is a data-driven approach that can capture highly compact hierarchical non-linear relationships among high-dimensional features, and therefore can facilitate the development of clinical tools for making a more accurate and earlier diagnosis of schizophrenia.
Aims
To identify consistent grey matter abnormalities in patients with schizophrenia, 662 people with schizophrenia and 613 healthy controls were recruited from eight centres across China, and the data from these independent sites were used to validate deep-learning classifiers.
Method
We used a prospective image-based meta-analysis of whole-brain voxel-based morphometry. We also automatically differentiated patients with schizophrenia from healthy controls using combined grey matter, white matter and cerebrospinal fluid volumetric features, incorporated a deep neural network approach on an individual basis, and tested the generalisability of the classification models using independent validation sites.
Results
We found that statistically reliable schizophrenia-related grey matter abnormalities primarily occurred in regions that included the superior temporal gyrus extending to the temporal pole, insular cortex, orbital and middle frontal cortices, middle cingulum and thalamus. Evaluated using leave-one-site-out cross-validation, the performance of the classification of schizophrenia achieved by our findings from eight independent research sites were: accuracy, 77.19–85.74%; sensitivity, 75.31–89.29% and area under the receiver operating characteristic curve, 0.797–0.909.
Conclusions
These results suggest that, by using deep-learning techniques, multidimensional neuroanatomical changes in schizophrenia are capable of robustly discriminating patients with schizophrenia from healthy controls, findings which could facilitate clinical diagnosis and treatment in schizophrenia.
The function and change of global soil carbon (C) reserves in natural ecosystems are key regulators of future carbon-climate coupling. Microbes play a critical role in soil carbon cycling and yet there is poor understanding of their roles and C metabolism flexibility in many ecosystems. We wanted to determine whether vegetation type and climate zone influence soil microbial community composition (fungi and bacteria) and carbon resource preference. We used a biomarker (phospholipid fatty acids, PLFAs), natural abundance 13C and 14C probing approach to measure soil microbial composition and C resource use, along a 1900–4167-m elevation gradient on Mount Gongga (7556 m asl), China. Mount Gongga has a vertical mean annual temperature gradient of 1.2–10.1°C and a diversity of typical vegetation zones in the Tibetan Plateau. Soils were sampled at 10 locations along the gradient capturing distinct vegetation types and climate zones from lowland subtropical-forest to alpine-meadow. PLFA results showed that microbial communities were composed of 2.1–51.7% bacteria and 2.0–23.2% fungi across the elevation gradient. Microbial biomass was higher and the ratio of soil fungi to bacteria (F/B) was lower in forest soils compared to meadow soils. δ13C varied between −33‰ to −17‰ with C3 plant carbon sources dominant across the gradient. Soil organic carbon (SOC) turnover did not vary among three soils we measured from three forest types (i.e., evergreen broadleaved subtropical, mixed temperate, coniferous alpine) and dissolved organic carbon (DOC) turnover decreased with soil elevation. Forest soil microbial PLFA 14C and δ13C measurements showed that forest type and climate were related to different microbial C use. The 14C values of microbial PLFAs i15, a15, 16:1, br17 decreased with elevation while those of C16:0, cyC17, and cyC19 did not show much difference among three forest ecosystems. Bacteria and bacillus represented by C16:1 and brC17 showed considerable microbial C metabolism flexibility and tended to use ancient carbon at higher altitudes. Anaerobes represented by cyC17 and cyC19 showed stronger C metabolism selectivity. Our findings reveal specific C source differences between and within soil microbial groups along elevation gradients.
Cystic echinococcosis (CE) occurs in the intermediate host's liver, assuming a bladder-like structure surrounded by the host-derived collagen capsule mainly derived from activated hepatic stellate cells (HSCs). However, the effect of CE on liver natural killer (NK) cells and the potential of transforming growth factor-β (TGF-β) signalling inhibition on alleviating CE-related liver damage remain to be explored. Here, by using the CE-mouse model, we revealed that the inhibitory receptors on the surface of liver NK cells were up-regulated, whereas the activating receptors were down-regulated over time. TGF-β1 secretion was elevated in liver tissues and mainly derived from macrophages. A combination of TGF-β signalling inhibitors SB525334 and pirfenidone could reduce the expression of TGF-β1 signalling pathway-related proteins and collagen production. Based on the secretion of TGF-β1, only the pirfenidone group showed a depressing effect. Also, the combination of SB525334 and pirfenidone exhibited a higher potential in effectively alleviating the senescence of the hepatocytes and restoring liver function. Together, TGF-β1 may be a potential target for the treatment of CE-associated liver fibrosis.
Solid solution 0.94Na0.5Bi0.5TiO3–6BaTiO3 (NBT–6BT) is considered to be one kind of lead-free piezoelectric materials with excellent electrical properties due to the existence of morphotropic phase boundary (MPB). However, its relatively lower depolarization temperature is a long-standing bottleneck for the application of NBT-based piezoelectric ceramics. In this work, the influence of thermal quenching on depolarization temperature and electrical properties of rare-earth Ho-doped NBT–6BT lead-free ceramics was investigated. It was shown that the relative high piezoelectric performance, as well as an improvement of depolarization temperature (Td), can be realized by thermal quenching. The results showed that the quenching process induced high concentration of oxygen vacancy, giving rise to the change of octahedra mode and enhanced lattice distortion, which is benefit to the temperature stability of piezoelectric and ferroelectric properties. Furthermore, up-conversion photoluminescence (PL) of Ho-doped NBT–6BT could be effectively tuned by the introduction of oxygen vacancy, suggesting a promising potential in optical–electrical multifunctional devices.
The present study investigated the association between fibre degradation and the concentration of dissolved molecular hydrogen (H2) in the rumen. Napier grass (NG) silage and corn stover (CS) silage were compared as forages with contrasting structures and degradation patterns. In the first experiment, CS silage had greater 48-h DM, neutral-detergent fibre (NDF) and acid-detergent fibre degradation, and total gas and methane (CH4) volumes, and lower 48-h H2 volume than NG silage in 48-h in vitro incubations. In the second experiment, twenty-four growing beef bulls were fed diets including 55 % (DM basis) NG or CS silages. Bulls fed the CS diet had greater DM intake (DMI), average daily gain, total-tract digestibility of OM and NDF, ruminal dissolved methane (dCH4) concentration and gene copies of protozoa, methanogens, Ruminococcus albus and R. flavefaciens, and had lower ruminal dH2 concentration, and molar proportions of valerate and isovalerate, in comparison with those fed the NG diet. There was a negative correlation between dH2 concentration and NDF digestibility in bulls fed the CS diet, and a lack of relationship between dH2 concentration and NDF digestibility with the NG diet. In summary, the fibre of CS silage was more easily degraded by rumen microorganisms than that of NG silage. Increased dCH4 concentration with the CS diet presumably led to the decreased ruminal dH2 concentration, which may be helpful for fibre degradation and growth of fibrolytic micro-organisms in the rumen.
The Wulian complex is located on the northern margin of the Sulu orogenic belt, and was formed by collision between the North China Craton (NCC) to the north and South China Craton (SCC) to the south. It consists of the metasedimentary Wulian Group, gneissic granite and meta-diorite. The U–Pb analyses for the detrital zircons from the Wulian Group exhibit one predominant age population of 2600–2400 Ma with a peak at c. 2.5 Ga and several secondary age populations of > 3000, 3000–2800, 2800–2600, 2200–2000, 1900–1800, 1500–1300 and 1250–950 Ma; some metamorphic zircons have metamorphic ages of c. 2.7, 2.55–2.45, 2.1–2.0 and 1.95–1.80 Ga, which are consistent with magmatic-metamorphic events in the SCC. Additionally, the Wulian Group was intruded by the gneissic granite and meta-diorite at c. 0.76 Ga, attributed to Neoproterozoic syn-rifting bimodal magmatic activity in the SCC and derived from partial melting of Archaean continental crust and depleted mantle, respectively. The Wulian Group therefore has tectonic affinity to the SCC and was mainly sourced from the SCC. The detrital zircons have positive and negative ϵHf(t) values, indicating that their source rocks were derived from reworking of both ancient and juvenile crustal rocks. The major early Precambrian crustal growth took place during c. 3.4–2.5 Ga with a dominant peak at 2.96 Ga and several secondary peaks at 3.27, 2.74 and 2.52 Ga. The two oldest zircons with ages of 3307 and 3347 Ma record the recycling of ancient continental crust (> 3.35 Ga) and crustal growth prior to c. 3.95 Ga in the SCC.
Emerging evidence has been revealed that high fat diet (HFD) correlate with insulin resistance (IR) which could be induced by endoplasmic reticulum stress (ERS). Recently, obesity or HFD induced nonalcoholic fatty liver disease (NAFLD) could promote alteration of iron metabolism. Disorder of iron metabolism have been linked to unnormal metabolism of glucose and lipid. Herein, we investigated the effect of impaired iron homeostasis on hepatic IR, focusing on ferritinophagy. Male C57/6J mice were administered with HFD (60% energy from fat) or LFD (10% energy from fat) for 10 weeks (n = 10), and Palmitic acid (PA)-insulin treated HepG2 cells were also established. Hepatic IR as evidenced by increased hepatic steatosis and decreased of p-AKT (48%, p < 0.0005), p-GSK-3β (34%, p < 0.05) in the liver of HFD mice. In addition, decreased iron level and expression NCOA4, as well as increased up-regulation of IRE1α and EIF2α were observed in HFD liver. By using desferrioxamine (DFO) and ferric ammonium citrate (FAC), we examined iron level on IRE1α and EIF2α. And glucose uptake assay shown that FAC supplementation, and ERS inhibitors of 4-PBA and STF could improve the glucose uptake of HepG2 cells in the presence of PA. Furthermore, we evaluated the glucose uptake of HepG2 cells incubated with adenovirus which mediated overexpression of NCOA4, FAC, 4-PBA (ERS inhibitor) or STF (IRE1 inhibitor). Taken together, deficiency of iron induced by impaired ferritinophagy induced hepatic IR, partly by aggravating hepatic ERS, especially IRE1 signal pathway in vivo and vitro. These findings provide evidence and new insight for therapeutic strategy of iron deficiency in NAFLD.
This article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.
Homology surveillance of carbapenem-resistant Klebsiella pneumoniae (CRKP) is critical to monitor and prevent outbreaks of nosocomial infections. In the present study, a matrix-assisted laser desorption/ionisation-time of flight (MALDI-TOF MS)-based method was evaluated as a rapid tool for typing CRKP in comparison with pulsed-field gel electrophoresis (PFGE) and multi locus sequence typing (MLST). Drug-resistant phenotypes and genotypes of 44 CRKP isolates were detected by microdilution broth method and polymerase chain reaction, and typed by PFGE, MLST and MALDI-TOF MS. Simpson's Index of Diversity was used to evaluate taxonomic diversity, Adjusted Rand Index (ARI) for congruence between the typing methods and Wallace coefficients (W) for the ability of either method to predict each other. Forty-four CRKP isolates of 15 sequence types (STs) produced either NDM-1 (n = 16), NDM-5 (n = 9) or KPC-2 (n = 19) carbapenemases. PFGE differentiated these isolates into 16 distinct types, and two deoxyribonucleic acid profiles were assigned to ST337 and ST11, respectively. MALDI-TOF MS failed to clearly delineate between clusters on dendrograms based on principal components analysis and main spectrum profile. The chosen parameters resulted in a maximum ARI of 0.310 (95% CI 0.088–0.531) between MALDI-TOF MS typing and the PFGE reference, indicating a low ability of the former to correctly identify related isolates. Likewise, the maximum W coefficient of 0.367 (95% CI 0.203–0.532) showed that MALDI-TOF MS had a lower predictive power than PFGE. We conclude that MALDI-TOF MS lacks the discriminatory power necessary for clone assignment of CRKP isolates and consequently cannot be considered as a rapid and creditable method for this purpose.
To explore whether and how group cognitive-behavioural therapy (GCBT) plus medication differs from medication alone for the treatment of generalised anxiety disorder (GAD).
Methods:
Hundred and seventy patients were randomly assigned to the GCBT plus duloxetine (n=89) or duloxetine group (n=81). The primary outcomes were Hamilton Anxiety Scale (HAMA) response and remission rates. The explorative secondary measures included score reductions from baseline in the HAMA total, psychic, and somatic anxiety subscales (HAMA-PA, HAMA-SA), the Hamilton Depression Scale, the Severity Subscale of Clinical Global Impression Scale, Global Assessment of Functioning, and the 12-item Short-Form Health Survey. Assessments were conducted at baseline, 4-week, 8-week, and 3-month follow-up.
Results:
At 4 weeks, HAMA response (GCBT group 57.0% vs. control group 24.4%, p=0.000, Cohen’s d=0.90) and remission rates (GCBT group 21.5% vs. control group 6.2%, p=0.004; d=0.51), and most secondary outcomes (all p<0.05, d=0.36−0.77) showed that the combined therapy was superior. At 8 weeks, all the primary and secondary significant differences found at 4 weeks were maintained with smaller effect sizes (p<0.05, d=0.32−0.48). At 3-month follow-up, the combined therapy was only significantly superior in the HAMA total (p<0.045, d=0.43) and HAMA-PA score reductions (p<0.001, d=0.77). Logistic regression showed superiority of the combined therapy for HAMA response rates [odds ratio (OR)=2.12, 95% confidence interval (CI) 1.02−4.42, p=0.04] and remission rates (OR=2.80, 95% CI 1.27−6.16, p=0.01).
Conclusions:
Compared with duloxetine alone, GCBT plus duloxetine showed significant treatment response for GAD over a shorter period of time, particularly for psychic anxiety symptoms, which may suggest that GCBT was effective in changing cognitive style.
Suppose that $0<|\unicode[STIX]{x1D70C}|<1$ and $m\geqslant 2$ is an integer. Let $\unicode[STIX]{x1D707}_{\unicode[STIX]{x1D70C},m}$ be the self-similar measure defined by $\unicode[STIX]{x1D707}_{\unicode[STIX]{x1D70C},m}(\cdot )=\frac{1}{m}\sum _{j=0}^{m-1}\unicode[STIX]{x1D707}_{\unicode[STIX]{x1D70C},m}(\unicode[STIX]{x1D70C}^{-1}(\cdot )-j)$. Assume that $\unicode[STIX]{x1D70C}=\pm (q/p)^{1/r}$ for some $p,q,r\in \mathbb{N}^{+}$ with $(p,q)=1$ and $(p,m)=1$. We prove that if $(q,m)=1$, then there are at most $m$ mutually orthogonal exponential functions in $L^{2}(\unicode[STIX]{x1D707}_{\unicode[STIX]{x1D70C},m})$ and $m$ is the best possible. If $(q,m)>1$, then there are any number of orthogonal exponential functions in $L^{2}(\unicode[STIX]{x1D707}_{\unicode[STIX]{x1D70C},m})$.