Business Execution Consultant 4 - Contingent Pinnacle Technical ResourcesBusiness Execution Consultant 4 - ContingentChandler, Arizona$58–$68 / hourContractorThe specific compensation for this position will be determined by a number of factors, including the scope, complexity and location of the role as well as the cost of labor in the market; the skills, education, training, credentials and experience of the candidate; and other conditions of employment. Required Qualifications:5 plus years of Business Execution, Implementation, or Strategic Planning experience, or equivalent demonstrated through one or a combination of the following: work or consulting experience, training, military experience, education.
Process Governance Consultant BC ForwardProcess Governance ConsultantChandler, AZ$88–$88.02 / hourFull timeThe ideal candidate will have strong experience in enterprise process management, operational risk governance, and cross-functional stakeholder engagement and a proven ability to drive process improvements, ensure policy adherence, and deliver measurable outcomes. With delivery centers and offices across North America and India, we take pride in building long-term relationships and delivering excellence through innovation, collaboration, and integrity.
Sales Engineer NucorSales EngineerPhoenix, AZ$98,238.40–$131,643.20 / yearThe successful candidate will be a relationship-driven professional who thrives on connecting with contractors, structural engineers, and architects to promote innovative framing and decking solutions that deliver value to building projects. Vulcraft and Verco Decking, divisions of Nucor Corporation, are leading manufacturers of steel joists and decking products serving the Western U.S. market.
NewField Sales Engineer - West OMI Industries IncField Sales Engineer - WestPhoenix, AZThis is a hands-on, traveling role (up to 30-50% overnight travel) that requires a strong combination of creative thinking and quantitative skills to identify growth opportunities, define strategy, and implement programs that are both brand building and metrics driven. Visit potential customers on site to demonstrate applications, teach them about products, how to select proper chemistry, source an odor, address an odor, and how an application system would be designed to distribute product.
NewRegional Sales Engineer- Inpro/Seal Dover Precision ComponentsRegional Sales Engineer- Inpro/SealPhoenix, AZ$110,000–$145,000Our strong Company portfolio is comprised of long products and services offered under Cook Compression, Cook Mechanical Field Services, Waukesha Bearings, Waukesha Magnetic Bearings, Inpro/Seal, Bearings Plus, and FW Murphy Production Controls. Dover Precision Components delivers products and services that enhance performance, improve safety, reduce carbon emissions, and accelerate clean energy adoption, through collaborative Customer relationships, expert engineering, and an innovative culture.
Managing Technical Consultant, Environmental Hydrogeologist ERM International Group LtdManaging Technical Consultant, Environmental HydrogeologistScottsdale, AZAs a Managing Technical Consultant, Environmental Hydrogeologist with specialized groundwater modeling expertise, you will deliver high-quality, defensible work that directly shapes sustainable outcomes in mining, water supply, energy, manufacturing, and beyond. Who We Are: As the largest global pure play sustainability consultancy, we partner with the world's leading organizations, creating innovative solutions to sustainability challenges and unlocking commercial opportunities that meet the needs of today while preserving opportunity for future generations.
Sr Mainframe Technical Consultant Broadcom IncSr Mainframe Technical ConsultantAZ$100,000–$160,000 / yearOverall, this position is responsible for delivering positive, quantifiable results for Broadcom measured across five primary areas: Customer Focus: Effectively and compellingly communicate Broadcom's key capabilities to address customer and partner needs. Displaying a broad range of disciplines, environments, and best practices within the mainframe operations practice or, the individual may possess skills and highly technical experience in Broadcom Software mainframe products e.g.
Principal Technical Consultant - Paradox Workday IncPrincipal Technical Consultant - ParadoxScottsdale, AZ$147,400–$221,000 / yearWe know that flexibility can take shape in many ways, so rather than a number of required days in-office each week, we simply spend at least half (50%) of our time each quarter in the office or in the field with our customers, prospects, and partners (depending on role). Leading improvements and Enabling our sales and engineering process (via tools, processes, and other initiatives), Creating documentation, whitepapers, and other supporting material for internal and client usage.
Senior Digital Technical Consultant Pyramid, IncSenior Digital Technical ConsultantPhoenix, AZ$84–$88 / hourFull timeDocument development processes, code changes, and system configurations for future referenceKey Requirements and Technology Experience: Key Skills; Customer Engage, Producer Engage, Jutro Proven experience as a Digital Technical Developer and leader, with a strong focus on the Jutro Digital Platform. By applying to our jobs you agree to receive calls, AI-generated calls, text messages, or emails from Pyramid Consulting, Inc. and its affiliates, and contracted partners.
NewManaging Technical Consultant, Archaeologist - Arizona ERM International Group LtdManaging Technical Consultant, Archaeologist - ArizonaScottsdale, AZOwn the impact of cultural resource stewardship-lead complex archaeological projects that shape sustainable development across the U.S. This is an opportunity to step into a leadership role where your expertise not only shapes projects-but helps preserve cultural history while enabling future development. Who We Are: As the largest global pure play sustainability consultancy, we partner with the world's leading organizations, creating innovative solutions to sustainability challenges and unlocking commercial opportunities that meet the needs of today while preserving opportunity for future generations.
NewManaging Technical Consultant, Archaeologist - Arizona ERMManaging Technical Consultant, Archaeologist - ArizonaScottsdale, ArizonaAs the largest global pure play sustainability consultancy, we partner with the world’s leading organizations, creating innovative solutions to sustainability challenges and unlocking commercial opportunities that meet the needs of today while preserving opportunity for future generations. Our diverse team of world-class experts supports clients across the breadth of their organizations to operationalize sustainability, underpinned by our deep technical expertise in addressing their environmental, health, safety, risk and social issues.
Crowdstrike Technical Consultant Accenture PlcCrowdstrike Technical ConsultantScottsdale, AZYou will work alongside Accenture's CrowdStrike Business Group as a trusted technical expert, supporting pre-sales engagements with deep platform knowledge and experience in hands-on delivery of CrowdStrike Falcon platform implementations for enterprise clients. Accenture provides the opportunity to support world-class cybersecurity programs for some of the largest organizations in the world, through a focus on rapid threat identification, incident response, cyber threat intelligence infusion, and mitigations to ensure defensive resiliency.
Autonomous Haulage Systems (AHS) Mining Technical Consultant - (Job Number: CAL01UW) WorleyParsonsAutonomous Haulage Systems (AHS) Mining Technical Consultant - (Job Number: CAL01UW)Phoenix, AZstrong>Primary Location: USA-CO-Denver, USA-UT-Salt Lake City, CAN-BC-Vancouver, CAN-ON-Toronto, USA-TX-Houston, USA-AZ-Phoenix. Unposting Date: Director, Autonomous Operations.
Senior Consultant-Transmission & Distribution (T&D) Technical Services Guidehouse IncSenior Consultant-Transmission & Distribution (T&D) Technical ServicesAZ$80,000–$133,000 / yearSenior Consultant - Bachelor's degree in Electrical Engineering or Power Systems Engineering AND 3+ years United States Bulk Electric System (BES) professional work experience excluding internships, co-ops, or fellowships; Or Master's degree in Electrical Engineering or Power Systems Engineering AND 1+ years United States Bulk Electric System (BES) professional work experience excluding internships, co-ops, or fellowships; Or Completing a PhD degree in electrical or power systems engineering from an accredited university or college in 2026 AND One (1+) plus year directly relevant Graduate Assistant/Research work with relevant PhD research/course work experience. Managing Consultant - Bachelor's degree in Electrical Engineering or Power Systems Engineering AND 5+ years United States Bulk Electric System (BES) professional work experience excluding internships, co-ops, or fellowships; Or Master's degree in Electrical Engineering or Power Systems Engineering AND 3+ years United States Bulk Electric System (BES) professional work experience excluding internships, co-ops, fellowships; Or PhD degree in Electrical Engineering or Power Systems Engineering AND 1+ years United States Bulk Electric System (BES) professional work experience excluding internships, co-ops or fellowships.
Technical Commerce & AI Consultant | Agentic Commerce Accenture PlcTechnical Commerce & AI Consultant | Agentic CommerceScottsdale, AZWithin Song, the Customer Technology - Commerce practice helps organizations design, build, and scale modern digital commerce ecosystems that deliver personalized, seamless, and intelligent customer experiences. By embedding Generative AI and Agentic AI into commerce operations, we enable real-time personalization, autonomous merchandising, dynamic pricing, campaign orchestration, and revenue growth at scale.
Consultant, Workday HCM Technical - Top Secret Cleared Deloitte Touche Tohmatsu LtdConsultant, Workday HCM Technical - Top Secret ClearedAZ$78,700–$155,100 / yearAs a Consultant on the team, you will be responsible for: Providing technical design and architecture support for Workday Human Capital Management (HCM) implementations by translating requirements into scalable, secure solutions aligned with Workday leading practices. Supporting integration design and delivery across APIs, Enterprise Interface Builder (EIB), connectors, and file-based integrations by contributing to technical design artifacts, build guidance, and test/defect triage.
Delivery Consultant, Technical Change Management Deloitte Touche Tohmatsu LtdDelivery Consultant, Technical Change ManagementGilbert, AZ2+ years of experience supporting organizational change management initiatives, including communications, training, change readiness assessments, impact assessments, stakeholder management, or leadership alignment, in a consulting environment or industry setting. Our Organization, Workforce, & Change offering shapes market-leading organizational strategies, delivers impactful change, and generates client value through the workforce, while leveraging data-driven insights and exceptional delivery execution.
Delivery Consultant, Oracle HCM Technical Deloitte Touche Tohmatsu LtdDelivery Consultant, Oracle HCM TechnicalGilbert, AZCenter Location & Travel Requirements: Hybrid Work Model: Operate under a hybrid system requiring residence within a commutable distance to one of the Center locations (Gilbert, Lake Mary, or Mechanicsburg) or Geo-Hub locations (Atlanta, Charlotte, Dallas, Houston, and Philadelphia). Co-location Expectation: Spend up to 30% of working time co-located at an assigned office for orchestrated opportunities, including projects, practice sessions, training, and Moments That Matter at a Deloitte Center location, Geo-Hub location, approved site, or project location.
Oracle Technical Cloud Senior Consultant Deloitte Touche Tohmatsu LtdOracle Technical Cloud Senior ConsultantTempe, AZ$110,700–$218,300 / yearThe wage range for this role takes into account the wide range of factors that are considered in making compensation decisions including but not limited to skill sets; experience and training; licensure and certifications; and other business and organizational needs. 1+ year of experience working with commercial cloud platforms such as Oracle Cloud Infrastructure (OCI), Amazon Web Services (AWS), Microsoft Azure, or Google Cloud Platform (GCP).
Senior Consultant, Oracle HCM Technical Deloitte Touche Tohmatsu LtdSenior Consultant, Oracle HCM TechnicalTempe, AZ$110,700–$218,300 / yearOur HR Strategy & Technology offering develops leading global HR strategies and implements HR technologies that drive transformation, maximize the workforce experience, and sustain HR effectiveness and value while navigating a world of disruption. Our purpose comes through in our work with clients that enables impact and value in their organizations, as well as through our own investments, commitments, and actions across areas that help drive positive outcomes for our communities.
Technical Client Consultant JPMorgan Chase & CoTechnical Client ConsultantTempe, AZOur history spans over 200 years and today we are a leader in investment banking, consumer and small business banking, commercial banking, financial transaction processing and asset management. JPMorganChase, one of the oldest financial institutions, offers innovative financial solutions to millions of consumers, small businesses and many of the worlds most prominent corporate, institutional and government clients under the J.P.
Technical Consultant Casualty Claims- CGL The Hanover Insurance Group IncTechnical Consultant Casualty Claims- CGLAZDigital Fluency: Effectively uses digital tools and technology appropriately to find, evaluate, create, and communicate information understands how to navigate digital platforms, use software applications, and leverage technology for productivity and communication purposes. Customer Centricity: Makes customers/clients and their needs a primary focus of one's actions; shows interest in and understanding of the needs and expectations of internal and external customers; gains customer trust and respect; meets or exceeds customer expectations.
Capital Projects Technical Senior Consultant - Procore Deloitte Touche Tohmatsu LtdCapital Projects Technical Senior Consultant - ProcoreAZ$110,700–$218,300 / yearFrom strategy to execution, this team delivers integrated, end-to-end support and advisory services covering valuation modeling, cost optimization, restructuring, business design and transformation, infrastructure and real estate, mergers and acquisitions (M&A), and sustainability. Work alongside clients every step of the way, helping them navigate new challenges, avoid financial pitfalls, and provide practical solutions at every stage of their journey-before, during, and after any major transformational projects or transactions.
Microsoft D365 F&O Technical Sr Consultant Deloitte Touche Tohmatsu LtdMicrosoft D365 F&O Technical Sr ConsultantAZ$116,000–$229,100 / yearAs a Dynamics 365 Finance & Operations Developer, you will manage the technical workstreams of end-to-end implementations of D365 F&O, review functional and craft technical documentation, develop integrations, data migrations, collaborate through testing phases. Our purpose comes through in our work with clients that enables impact and value in their organizations, as well as through our own investments, commitments, and actions across areas that help drive positive outcomes for our communities.
Sr Risk Control Consultant United Fire Group IncSr Risk Control ConsultantAZ$112,000–$143,000 / yearThe Senior Risk Control or Technical Consultant is a risk management professional who will focus on risk assessment and service work, providing leadership in division/branch-level underwriting, claims, agency distribution, and strategic planning meetings and initiatives, and acting as a Risk Control liaison to agency partners within their assigned territory. Core Competencies Advanced technical risk assessment Strategic and consultative thinking High-quality technical writing Collaboration with underwriting and stakeholders Mentorship and leadership Continuous improvement mindset Working Conditions: 60 % field work and 40% remote work environment with 20% regional travel as needed.
NewSales Consultant Zelus UsaSales ConsultantPhoenix, ArizonaThis role requires proven success selling BIM/VDC, mechanical, electrical, or other construction-related solutions, combined with a consultative sales approach that positions the company as a trusted industry partner. The Construction Consultant will be responsible for expanding market presence and driving revenue growth by cultivating strong relationships with clients in construction, distribution, retail, and related vertical markets.
Industrial Cybersecurity Senior Consultant Black & Veatch Holding CoIndustrial Cybersecurity Senior ConsultantPhoenix, AZThe Industrial Cybersecurity Senior Consultant manages or contributes to technical consulting projects and implementation services for critical infrastructure clients. As employee-owners, our professionals are empowered to drive not only their personal growth, but the companys long-term achievements - and they share in the financial rewards of the success through stock ownership.
Commercial Sales Consultant Guild Garage GroupCommercial Sales ConsultantMesa, AZ$70,000–$150,000 / yearPay Range$70,000—$150,000 USDBy submitting your application, you consent to receive text messages, emails, and phone calls from Guild Garage Group and/or our coalition of partnered brands regarding job opportunities, application status, and recruiting-related communications. As a fast-growing garage door brand with a sterling reputation across Arizona, we're expanding our commercial division — and we're looking for an experienced, driven Commercial Door Sales Consultant to lead that growth.
Commercial Sales Consultant Goody Garage DoorsCommercial Sales ConsultantMesa, AZ$70,000–$150,000 / yearPay Range$70,000—$150,000 USDBy submitting your application, you consent to receive text messages, emails, and phone calls from Guild Garage Group and/or our coalition of partnered brands regarding job opportunities, application status, and recruiting-related communications. As a fast-growing garage door brand with a sterling reputation across Arizona, we're expanding our commercial division — and we're looking for an experienced, driven Commercial Door Sales Consultant to lead that growth.
Managing Consultant, Mining Services ERMManaging Consultant, Mining ServicesScottsdale, Arizona$90,810–$124,245 / yearSupport mining projects throughout their entire lifecycle, including activities such as project permitting, conducting regulatory audits, facilitating environmental compliance, assisting with operational best practices, drafting closure plans, overseeing sampling and field work campaigns and contributing to project assessments and reviews. As the largest global pure play sustainability consultancy, we partner with the world’s leading organizations, creating innovative solutions to sustainability challenges and unlocking commercial opportunities that meet the needs of today while preserving opportunity for future generations.
Solutions Consultant 2 - SLED Palo Alto Networks Public SectorSolutions Consultant 2 - SLEDPhoenix, ArizonaThe Solutions Consultant is the evolution of the traditional Sales Engineering role, aligning how we best serve our customers in understanding their environment, providing solution guidance and ensuring value realization in their investment with Palo Alto Networks. Demonstrating strong communication skills, influencing through effective presentations and customer-specific demos, and conducts technical engagements and workshops that are clear and impactful, simplifying complex ideas for various audiences.
CFO Consultant NOW CFOCFO ConsultantPhoenix, AZ$190,000–$210,000 / yearCandidates must have 10 or more years of experience in a CFO or senior financial leadership role, with demonstrated expertise in GAAP, financial reporting, audit management, and internal controls. The CFO consultant will be responsible for overseeing all financial aspects of client organizations while providing strategic guidance on technology and data-driven initiatives.
Senior Technical Support Engineer - Mainframe 74Software SASenior Technical Support Engineer - MainframeScottsdale, AZRemoteWe are recognized as global industry leaders, helping organizations drive digital transformation with secure, mission-critical software that powers impactful business outcomes. Must have deep knowledge of network connectivity and communication protocols such as FTP/SFTP, HTTP/HTTPS, SSH, and TLS certificate management.
Senior Technical Support Engineer – Mainframe Axway Software SASenior Technical Support Engineer – MainframeScottsdale, ArizonaRemoteWe are recognized as global industry leaders, helping organizations drive digital transformation with secure, mission-critical software that powers impactful business outcomes. Must have deep knowledge of network connectivity and communication protocols such as FTP/SFTP, HTTP/HTTPS, SSH, and TLS certificate management.
Technical Sales Manager - Southwest Atkore IncTechnical Sales Manager - SouthwestTempe, AZ$126,800–$174,350 / yearHave met all of your Atkore Contractor Elite (ACE Contractors) Within 12 months, you'll: Identify additional ACE Contractors within your Region Be able conduct all available Certified Installer Trainings for Contractors Know all of your Atkore Strategic Agents in your Region Complete specifications reviews with Engineering Firms in your Region for all of Atkore Electrical Products (EP). Who we are looking for: We are currently searching for a Technical Sales Manager to be based out of the Southwestern region of the U.S. Reporting to the Regional Vice President of Sales, this person will be responsible for generating specifications and preferences with a focus on end-users, Specifiers, and Electrical Contractors.
transmission-planning-consultant-1898-co-multiple-locations Burns & McDonnelltransmission-planning-consultant-1898-co-multiple-locationsPhoenix, AZ$110,000–$400,000 / yearBachelor Degree in Engineering or related degree from an ABET accredited program or related degree and 3 years of related experience required OR Master Degree in Engineering or Business and 2 years of experience required OR PhD in Engineering and 1 year of experience required. Perform a wide range of transmission planning and operational studies, including power flow, transient stability, transfer capability, short-circuit, voltage and reactive analysis, harmonics, EMT studies, reliability assessments, and production cost modeling.
Project Manager, Technology Consultant Stantec IncProject Manager, Technology ConsultantPhoenix, AZPrimary Location: United States | CA | Los Angeles Organization: 2804 Buildings-US West BSS-Los Angeles CA Employee Status: Regular Business Justification: New Position Travel: Yes Schedule: Full time Job Posting: 16/06/2026 03:06:48 Req ID: 1006295. Active member of the Technology Consulting Group in the U.S. West and is a part of multi-disciplined design teams for various sized projects in several markets, including Healthcare, Higher Education, Commercial and Government/Military.
R&D Tax Consultant McGuire SponselR&D Tax ConsultantGilbert, AZCredits are not limited to companies that solely provide product development — they are equally applicable to companies that develop new processes including improved efficiencies, as well as companies that invest in developing a new product or process for their customers. Ability to travel up to 30% independently or with a team to client sites across the U.S. Preferred but not required: prior R&D experience, familiarity with tax concepts, and consulting or client-facing experience.
R&D Tax Consultant - Technology Industry Lead McGuire SponselR&D Tax Consultant - Technology Industry LeadGilbert, AZCredits are not limited to companies that solely provide product development — they are equally applicable to companies that develop new processes including improved efficiencies, as well as companies that invest in developing a new product or process for their customers. Ability to travel up to 30% independently or with a team to client sites across the U.S. Preferred but not required: prior R&D experience, familiarity with tax concepts, and consulting or client-facing experience.
Senior Partner Solutions Consultant New Relic IncSenior Partner Solutions ConsultantPhoenix, AZRemote$203,000–$254,000 / yearPartner Enablement & Capability Building: Design and execute structured enablement plans for assigned partners, delivering workshops, "train-the-trainer" sessions, and technical coaching to close skill gaps and build technical autonomy. Solutioning & Pre-Sales Support: Act as an observability architect and "Swat Team" member for high-value partner-led opportunities, assisting with complex solution design, demonstrations, and Proofs of Value (POVs).
NewIT - Principal Consultant | Agile Management | Agile Management Tools Cloudspace LLCIT - Principal Consultant | Agile Management | Agile Management ToolsPhoenix, AZJob Title* Principal Consultant | Agile Management | Agile Management Tools. Detailed Job Description: Good Knowledge on Agile management tools.
NewIT - Lead Consultant | Cards and Payments | Cards Business Analysis Cloudspace LLCIT - Lead Consultant | Cards and Payments | Cards Business AnalysisPhoenix, AZ2.Connect with System Architect Engineering teamOther POs and Product Manager to develop and groom the team backlog. 1. Agile Product Owner experience 2. Credit Cards domain knowledge 3. Good Communication skills.
NewIT - Lead Consultant | Programing language C | go lang Cloudspace LLCIT - Lead Consultant | Programing language C | go langPhoenix, AZExperience with opensource frameworks is a plus especially maintaining or contributing to open source projects Experience with relational and NoSQL databases, including PostgreSQL, C. Detailed Job Description: Position requires a Bachelors degree in Computer Science, Engineering, or a related field followed by 6 years of experience in Golang development stack.
NewIT - Senior Associate Consultant | Development Methodology | Scrum Cloudspace LLCIT - Senior Associate Consultant | Development Methodology | ScrumPhoenix, AZDetailed Job Description: Candidate is responsible for lead daily standups, sprint planning, producing, maintaining, and improving technical documentation that supports developers, users, and stakeholders. This role ensures clarity, consistency, and accuracy across customer-facing, internal, and architectural documentation, working closely with engineering leadership.
NewIT - Lead Consultant | Java | J2EE Cloudspace LLCIT - Lead Consultant | Java | J2EEPhoenix, AZDetailed Job Description: JavaJ2EE full stack developer with financial or Banking domain experience. Job Details: Must Have Skills (Top 3 technical skills only) * .
Consultant | Java | Spring MVC IMCS Group IncConsultant | Java | Spring MVCPhoenix, AZCompany Description: IMCS Group is one of the fastest growing MWBE (Minority Woman Owned Enterprise) staffing firms in the U.S. We focus on bringing a Diversity Recruitment approach to Fortune 500 companies within North America and EMEA region contingent labor programs. Detailed Job Description: Strong technical knowledge on Java, Web Services, APIs, Spring, Spring Boot, Apache Camel, Hive, Spark, Hadoop.
Lead Consultant | Programing language C | go lang IMCS Group IncLead Consultant | Programing language C | go langPhoenix, AZCompany Description: IMCS Group is one of the fastest growing MWBE (Minority Woman Owned Enterprise) staffing firms in the U.S. We focus on bringing a Diversity Recruitment approach to Fortune 500 companies within North America and EMEA region contingent labor programs. Experience with opensource frameworks is a plus especially maintaining or contributing to open source projects Experience with relational and NoSQL databases, including PostgreSQL, C.
Energy & Special Projects Consultant GTN Technical StaffingEnergy & Special Projects ConsultantPhoenix, AZAccount Managers, focus their efforts on building and maintaining client relationships, keeping clients informed about the complete maintenance, repair, replacement, service and or energy efficiency package. We are a full-service HVAC, building automation, chiller, and retrofit contractor with a reputation for combining high-quality consulting services with customized energy solutions.
NewConsultant | Java | Spring MVC Ipolarity LLCConsultant | Java | Spring MVCPhoenix, AZDetailed Job Description: Strong technical knowledge on Java, Web Services, APIs, Spring, Spring Boot, Apache Camel, Hive, Spark, Hadoop. Participate in Scrum, for developing and deploying components.
NewLead Consultant, Due Diligence & Site Solutions Ramboll US CorporationLead Consultant, Due Diligence & Site SolutionsPhoenix, AZ$82,029–$102,536 / yearPrepare high-quality client deliverables, cost estimates, and proposals; coordinate with clients, regulators, subcontractors, and internal teams to execute projects and communicate findings; and travel for site visits/field assignments as needed. Support site investigations by developing scopes, coordinating fieldwork, collecting environmental samples (soil, groundwater, vapor, sediment, and surface/surface water), and interpreting analytical results.